![]() |
Boost-Commit : |
Subject: [Boost-commit] svn:boost r76092 - in trunk: boost/math/special_functions libs/math/doc/sf_and_dist libs/math/doc/sf_and_dist/equations libs/math/doc/sf_and_dist/html libs/math/doc/sf_and_dist/html/index libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders libs/math/doc/sf_and_dist/html/math_toolkit/dist libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg libs/math/doc/sf_and_dist/html/math_toolkit/extern_c libs/math/doc/sf_and_dist/html/math_toolkit/main_overview libs/math/doc/sf_and_dist/html/math_toolkit/perf libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint libs/math/doc/sf_and_dist/html/math_toolkit/special/expint libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper libs/math/doc/sf_and_dist/html/math_toolkit/special/powers libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc libs/math/doc/sf_and_dist/html/math_toolkit/special/zetas libs/math/doc/sf_and_dist/html/math_toolkit/status libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1 libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2 libs/math/doc/sf_and_dist/html/math_toolkit/using_udt libs/math/doc/sf_and_dist/html/math_toolkit/utils libs/math/doc/sf_and_dist/html/math_toolkit/utils/fp_facets libs/math/doc/sf_and_dist/html/math_toolkit/utils/next_float libs/math/doc/sf_and_dist/html/math_toolkit/utils/rounding libs/math/test
From: john_at_[hidden]
Date: 2011-12-21 11:08:00
Author: johnmaddock
Date: 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
New Revision: 76092
URL: http://svn.boost.org/trac/boost/changeset/76092
Log:
Update zeta implementation to use much faster algorithm.
Change zeta test to use external template instances.
Added:
trunk/libs/math/doc/sf_and_dist/equations/zeta6.mml (contents, props changed)
trunk/libs/math/doc/sf_and_dist/equations/zeta6.png (contents, props changed)
trunk/libs/math/doc/sf_and_dist/equations/zeta6.svg (contents, props changed)
trunk/libs/math/test/double_test_instances.cpp (contents, props changed)
trunk/libs/math/test/float_test_instances.cpp (contents, props changed)
trunk/libs/math/test/ldouble_test_instances.cpp (contents, props changed)
trunk/libs/math/test/real_concept_test_instances.cpp (contents, props changed)
Binary files modified:
trunk/libs/math/doc/sf_and_dist/equations/zeta1.png
trunk/libs/math/doc/sf_and_dist/equations/zeta1.svg
trunk/libs/math/doc/sf_and_dist/equations/zeta2.png
trunk/libs/math/doc/sf_and_dist/equations/zeta2.svg
trunk/libs/math/doc/sf_and_dist/equations/zeta3.svg
trunk/libs/math/doc/sf_and_dist/equations/zeta4.svg
trunk/libs/math/doc/sf_and_dist/equations/zeta5.svg
Text files modified:
trunk/boost/math/special_functions/zeta.hpp | 51 ++++++++
trunk/libs/math/doc/sf_and_dist/html/index.html | 4
trunk/libs/math/doc/sf_and_dist/html/index/s12.html | 2
trunk/libs/math/doc/sf_and_dist/html/index/s13.html | 2
trunk/libs/math/doc/sf_and_dist/html/index/s14.html | 2
trunk/libs/math/doc/sf_and_dist/html/index/s15.html | 2
trunk/libs/math/doc/sf_and_dist/html/index/s16.html | 2
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html | 90 +++++++-------
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html | 31 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html | 19 +-
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html | 6
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html | 56 ++++----
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html | 22 +-
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html | 37 ++---
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html | 75 ++++++------
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html | 98 +++++++--------
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html | 35 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html | 41 +++---
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html | 33 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html | 27 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html | 41 +++---
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html | 33 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/geometric_dist.html | 92 +++++++-------
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html | 31 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html | 43 +++---
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html | 33 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html | 42 +++---
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html | 31 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html | 35 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html | 31 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html | 35 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html | 43 +++---
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html | 35 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html | 35 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html | 91 +++++++-------
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html | 33 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html | 37 ++---
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html | 33 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html | 43 +++---
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html | 43 +++---
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html | 35 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/uniform_dist.html | 35 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/weibull_dist.html | 43 +++---
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/nmp.html | 162 +++++++++++++-------------
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/future.html | 28 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html | 4
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html | 14 --
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html | 42 +-----
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html | 6
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html | 21 --
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html | 2
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html | 29 +---
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html | 41 +-----
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html | 31 +---
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/geometric_eg.html | 65 +++-------
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/inverse_chi_squared_eg.html | 42 +++---
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html | 6
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html | 5
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html | 8
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html | 88 +++++---------
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html | 130 ++++++++++----------
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html | 101 ++++++----------
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html | 4
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html | 2
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html | 2
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html | 2
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/extern_c/c99.html | 13 +
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html | 33 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html | 21 +-
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/building.html | 18 +-
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html | 12
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html | 72 +++++-----
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html | 96 +++++++-------
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html | 18 +-
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html | 6
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/tr1.html | 32 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html | 66 +++++-----
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/assert_undefined.html | 2
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html | 58 ++++-----
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html | 52 ++++----
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html | 12 -
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/namespace_pol.html | 4
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/pol_ref_ref.html | 17 +-
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html | 96 +++++++-------
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/precision_pol.html | 5
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html | 1
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html | 20 +-
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/changing_policy_defaults.html | 5
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/namespace_policies.html | 21 --
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html | 69 +++++-----
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/user_def_err_pol.html | 19 ---
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html | 30 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html | 18 +-
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html | 30 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html | 30 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html | 31 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html | 31 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html | 35 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html | 34 ++---
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html | 36 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html | 35 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html | 31 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html | 19 +-
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html | 20 +-
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html | 32 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html | 19 +-
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html | 19 +-
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html | 23 +-
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html | 23 +-
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html | 23 +-
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html | 13 -
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html | 43 +++---
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html | 13 -
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html | 6
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html | 13 -
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html | 13 -
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html | 13 -
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html | 27 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html | 31 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html | 31 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html | 31 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html | 31 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html | 31 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html | 31 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_derivatives.html | 27 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html | 29 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html | 37 ++---
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html | 31 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html | 31 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html | 31 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html | 33 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html | 31 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html | 31 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html | 35 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html | 9
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinhc_pi.html | 9
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html | 41 ++---
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/status/history1.html | 96 +++++++-------
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/status/issues.html | 60 +++++----
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html | 47 +++---
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/constants.html | 13 -
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html | 19 +-
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html | 19 +-
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html | 41 +++---
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html | 241 +++++++++++++++++++--------------------
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html | 23 +-
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/tuples.html | 13 -
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html | 25 +--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html | 17 +-
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html | 62 +++++-----
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/using_udt/archetypes.html | 32 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/using_udt/concepts.html | 12
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/fp_facets.html | 12
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/examples.html | 28 +--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/intro.html | 34 ++--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/reference.html | 42 +++---
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/fpclass.html | 22 +-
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_advance.html | 13 -
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_distance.html | 13 -
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_next.html | 13 -
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_prior.html | 13 -
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/next_float/nextafter.html | 24 +--
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/rounding/modf.html | 1
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/rounding/round.html | 1
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/rounding/trunc.html | 1
trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/sign_functions.html | 36 ++--
trunk/libs/math/doc/sf_and_dist/zeta.qbk | 10 -
trunk/libs/math/test/Jamfile.v2 | 5
trunk/libs/math/test/pch.hpp | 7
trunk/libs/math/test/test_zeta.cpp | 3
trunk/libs/math/test/test_zeta.hpp | 2
171 files changed, 2552 insertions(+), 2860 deletions(-)
Modified: trunk/boost/math/special_functions/zeta.hpp
==============================================================================
--- trunk/boost/math/special_functions/zeta.hpp (original)
+++ trunk/boost/math/special_functions/zeta.hpp 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -89,6 +89,13 @@
return sum * 1 / -boost::math::powm1(T(2), sc);
}
+
+#if 0
+//
+// This code is commented out because we have a better more rapidly converging series
+// now. Retained for future reference and in case the new code causes any issues down the line....
+//
+
//
// Classical p-series:
//
@@ -119,12 +126,53 @@
policies::check_series_iterations<T>("boost::math::zeta_series2<%1%>(%1%)", max_iter, pol);
return result;
}
+#endif
+
+template <class T, class Policy>
+T zeta_polynomial_series(T s, T sc, Policy const &)
+{
+ //
+ // This is algorithm 3 from:
+ //
+ // "An Efficient Algorithm for the Riemann Zeta Function", P. Borwein,
+ // Canadian Mathematical Society, Conference Proceedings.
+ // See: http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf
+ //
+ BOOST_MATH_STD_USING
+ int n = itrunc(log(boost::math::tools::epsilon<T>()) / -2);
+ T sum = 0;
+ T two_n = ldexp(T(1), n);
+ int ej_sign = 1;
+ for(int j = 0; j < n; ++j)
+ {
+ sum += ej_sign * -two_n / pow(T(j + 1), s);
+ ej_sign = -ej_sign;
+ }
+ T ej_sum = 1;
+ T ej_term = 1;
+ for(int j = n; j <= 2 * n - 1; ++j)
+ {
+ sum += ej_sign * (ej_sum - two_n) / pow(T(j + 1), s);
+ ej_sign = -ej_sign;
+ ej_term *= 2 * n - j;
+ ej_term /= j - n + 1;
+ ej_sum += ej_term;
+ }
+ return -sum / (two_n * (1 - pow(T(2), sc)));
+}
template <class T, class Policy>
T zeta_imp_prec(T s, T sc, const Policy& pol, const mpl::int_<0>&)
{
BOOST_MATH_STD_USING
- T result;
+ T result;
+ if(fabs(sc) > 0.01f)
+ result = zeta_polynomial_series(s, sc, pol);
+ else
+ result = detail::zeta_series_imp(s, sc, pol);
+#if 0
+ // Old code archived for future reference:
+
//
// Only use power series if it will converge in 100
// iterations or less: the more iterations it consumes
@@ -135,6 +183,7 @@
result = detail::zeta_series2_imp(s, pol);
else
result = detail::zeta_series_imp(s, sc, pol);
+#endif
return result;
}
Modified: trunk/libs/math/doc/sf_and_dist/equations/zeta1.png
==============================================================================
Binary files. No diff available.
Modified: trunk/libs/math/doc/sf_and_dist/equations/zeta1.svg
==============================================================================
Binary files. No diff available.
Modified: trunk/libs/math/doc/sf_and_dist/equations/zeta2.png
==============================================================================
Binary files. No diff available.
Modified: trunk/libs/math/doc/sf_and_dist/equations/zeta2.svg
==============================================================================
Binary files. No diff available.
Modified: trunk/libs/math/doc/sf_and_dist/equations/zeta3.svg
==============================================================================
Binary files. No diff available.
Modified: trunk/libs/math/doc/sf_and_dist/equations/zeta4.svg
==============================================================================
Binary files. No diff available.
Modified: trunk/libs/math/doc/sf_and_dist/equations/zeta5.svg
==============================================================================
Binary files. No diff available.
Added: trunk/libs/math/doc/sf_and_dist/equations/zeta6.mml
==============================================================================
--- (empty file)
+++ trunk/libs/math/doc/sf_and_dist/equations/zeta6.mml 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -0,0 +1,185 @@
+<?xml version='1.0'?>
+<!DOCTYPE html PUBLIC '-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN'
+ 'http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd'
+ [<!ENTITY mathml 'http://www.w3.org/1998/Math/MathML'>]>
+<html xmlns='http://www.w3.org/1999/xhtml'>
+<head><title>zeta6</title>
+<!-- MathML created with MathCast Equation Editor version 0.89 -->
+</head>
+<body>
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+ <mrow>
+ <mi>ζ</mi>
+ <mfenced>
+ <mrow>
+ <mi>s</mi>
+ </mrow>
+ </mfenced>
+ <mspace width="1em"/>
+ <mo>=</mo>
+ <mspace width="1em"/>
+ <mfrac>
+ <mrow>
+ <mo>−</mo>
+ <mn>1</mn>
+ </mrow>
+ <mrow>
+ <msup>
+ <mi>s</mi>
+ <mi>n</mi>
+ </msup>
+ <mfenced>
+ <mrow>
+ <mn>1</mn>
+ <mo>−</mo>
+ <msup>
+ <mn>2</mn>
+ <mrow>
+ <mn>1</mn>
+ <mo>−</mo>
+ <mi>s</mi>
+ </mrow>
+ </msup>
+ </mrow>
+ </mfenced>
+ </mrow>
+ </mfrac>
+ <munderover>
+ <mo>∑</mo>
+ <mrow>
+ <mi>j</mi>
+ <mo>=</mo>
+ <mn>0</mn>
+ </mrow>
+ <mrow>
+ <mn>2</mn>
+ <mi>n</mi>
+ <mo>−</mo>
+ <mn>1</mn>
+ </mrow>
+ </munderover>
+ <mfrac>
+ <mrow>
+ <msub>
+ <mi>e</mi>
+ <mi>j</mi>
+ </msub>
+ </mrow>
+ <msup>
+ <mfenced>
+ <mrow>
+ <mi>j</mi>
+ <mo>+</mo>
+ <mn>1</mn>
+ </mrow>
+ </mfenced>
+ <mi>s</mi>
+ </msup>
+ </mfrac>
+ <mspace width="1em"/>
+ <mo>+</mo>
+ <mspace width="1em"/>
+ <mi>γ</mi>
+ <mfenced>
+ <mrow>
+ <mi>s</mi>
+ </mrow>
+ </mfenced>
+ <mspace width="1em"/>
+ <mo>;</mo>
+ <mspace width="1em"/>
+ <msub>
+ <mi>e</mi>
+ <mi>j</mi>
+ </msub>
+ <mo>=</mo>
+ <msup>
+ <mfenced>
+ <mrow>
+ <mo>−</mo>
+ <mn>1</mn>
+ </mrow>
+ </mfenced>
+ <mi>j</mi>
+ </msup>
+ <mfenced>
+ <mrow>
+ <munderover>
+ <mo>∑</mo>
+ <mrow>
+ <mi>k</mi>
+ <mo>=</mo>
+ <mn>0</mn>
+ </mrow>
+ <mrow>
+ <mi>j</mi>
+ <mo>−</mo>
+ <mi>n</mi>
+ </mrow>
+ </munderover>
+ <mfrac>
+ <mrow>
+ <mi>n</mi>
+ <mo>!</mo>
+ </mrow>
+ <mrow>
+ <mi>k</mi>
+ <mo>!</mo>
+ <mfenced>
+ <mrow>
+ <mi>n</mi>
+ <mo>−</mo>
+ <mi>k</mi>
+ </mrow>
+ </mfenced>
+ <mo>!</mo>
+ </mrow>
+ </mfrac>
+ <mo>−</mo>
+ <msup>
+ <mn>2</mn>
+ <mi>n</mi>
+ </msup>
+ </mrow>
+ </mfenced>
+ <mspace width="1em"/>
+ <mo>∧</mo>
+ <mspace width="1em"/>
+ <mo>|</mo>
+ <msub>
+ <mi>γ</mi>
+ <mi>n</mi>
+ </msub>
+ <mfenced>
+ <mrow>
+ <mi>s</mi>
+ </mrow>
+ </mfenced>
+ <mo>|</mo>
+ <mo><</mo>
+ <mo>=</mo>
+ <mfrac>
+ <mn>1</mn>
+ <mrow>
+ <msup>
+ <mn>8</mn>
+ <mi>n</mi>
+ </msup>
+ <mo>|</mo>
+ <mn>1</mn>
+ <mo>−</mo>
+ <msup>
+ <mn>2</mn>
+ <mrow>
+ <mn>1</mn>
+ <mo>−</mo>
+ <mi>s</mi>
+ </mrow>
+ </msup>
+ <mo>|</mo>
+ </mrow>
+ </mfrac>
+ </mrow>
+</math>
+</body>
+</html>
Added: trunk/libs/math/doc/sf_and_dist/equations/zeta6.png
==============================================================================
Binary file. No diff available.
Added: trunk/libs/math/doc/sf_and_dist/equations/zeta6.svg
==============================================================================
Binary file. No diff available.
Modified: trunk/libs/math/doc/sf_and_dist/html/index.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/index.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/index.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -52,7 +52,7 @@
<div><p class="copyright">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg</p></div>
<div><div class="legalnotice">
-<a name="id1029870"></a><p>
+<a name="math_toolkit.legal"></a><p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
</p>
@@ -513,7 +513,7 @@
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
-<td align="left"><p><small>Last revised: October 13, 2011 at 15:53:36 GMT</small></p></td>
+<td align="left"><p><small>Last revised: December 21, 2011 at 15:35:10 GMT</small></p></td>
<td align="right"><div class="copyright-footer"></div></td>
</tr></table>
<hr>
Modified: trunk/libs/math/doc/sf_and_dist/html/index/s12.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/index/s12.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/index/s12.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -24,7 +24,7 @@
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
-<a name="id1479273"></a>Function Index</h2></div></div></div>
+<a name="id1440372"></a>Function Index</h2></div></div></div>
<p><a class="link" href="s12.html#idx_id_0">A</a> <a class="link" href="s12.html#idx_id_1">B</a> <a class="link" href="s12.html#idx_id_2">C</a> <a class="link" href="s12.html#idx_id_3">D</a> <a class="link" href="s12.html#idx_id_4">E</a> <a class="link" href="s12.html#idx_id_5">F</a> <a class="link" href="s12.html#idx_id_6">G</a> <a class="link" href="s12.html#idx_id_7">H</a> <a class="link" href="s12.html#idx_id_8">I</a> <a class="link" href="s12.html#idx_id_9">K</a> <a class="link" href="s12.html#idx_id_10">L</a> <a class="link" href="s12.html#idx_id_11">M</a> <a class="link" href="s12.html#idx_id_12">N</a> <a class="link" href="s12.html#idx_id_14">P</a> <a class="link" href="s12.html#idx_id_15">Q</a> <a class="link" href="s12.html#idx_id_16">R</a> <a class="link" href="s12.html#idx_id_17">S</a> <a class="link" href="s12.html#idx_id_18">T</a> <a class="link" href="s12.html#idx_id_19">U</a> <a class="link" href="s12.html#idx_id_20">V</a> <a class="link" href="s12.html#idx_id_21">W</a> <a class="link" href=
"s12.html#idx_id_22">Z</a></p>
<div class="variablelist"><dl>
<dt>
Modified: trunk/libs/math/doc/sf_and_dist/html/index/s13.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/index/s13.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/index/s13.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -24,7 +24,7 @@
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
-<a name="id1494760"></a>Class Index</h2></div></div></div>
+<a name="id1456422"></a>Class Index</h2></div></div></div>
<p><a class="link" href="s13.html#idx_id_24">B</a> <a class="link" href="s13.html#idx_id_25">C</a> <a class="link" href="s13.html#idx_id_26">D</a> <a class="link" href="s13.html#idx_id_27">E</a> <a class="link" href="s13.html#idx_id_28">F</a> <a class="link" href="s13.html#idx_id_29">G</a> <a class="link" href="s13.html#idx_id_30">H</a> <a class="link" href="s13.html#idx_id_31">I</a> <a class="link" href="s13.html#idx_id_33">L</a> <a class="link" href="s13.html#idx_id_34">M</a> <a class="link" href="s13.html#idx_id_35">N</a> <a class="link" href="s13.html#idx_id_37">P</a> <a class="link" href="s13.html#idx_id_39">R</a> <a class="link" href="s13.html#idx_id_40">S</a> <a class="link" href="s13.html#idx_id_41">T</a> <a class="link" href="s13.html#idx_id_42">U</a> <a class="link" href="s13.html#idx_id_44">W</a></p>
<div class="variablelist"><dl>
<dt>
Modified: trunk/libs/math/doc/sf_and_dist/html/index/s14.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/index/s14.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/index/s14.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -24,7 +24,7 @@
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
-<a name="id1497858"></a>Typedef Index</h2></div></div></div>
+<a name="id1457335"></a>Typedef Index</h2></div></div></div>
<p><a class="link" href="s14.html#idx_id_46">A</a> <a class="link" href="s14.html#idx_id_47">B</a> <a class="link" href="s14.html#idx_id_48">C</a> <a class="link" href="s14.html#idx_id_49">D</a> <a class="link" href="s14.html#idx_id_50">E</a> <a class="link" href="s14.html#idx_id_51">F</a> <a class="link" href="s14.html#idx_id_52">G</a> <a class="link" href="s14.html#idx_id_53">H</a> <a class="link" href="s14.html#idx_id_54">I</a> <a class="link" href="s14.html#idx_id_56">L</a> <a class="link" href="s14.html#idx_id_58">N</a> <a class="link" href="s14.html#idx_id_59">O</a> <a class="link" href="s14.html#idx_id_60">P</a> <a class="link" href="s14.html#idx_id_62">R</a> <a class="link" href="s14.html#idx_id_63">S</a> <a class="link" href="s14.html#idx_id_64">T</a> <a class="link" href="s14.html#idx_id_65">U</a> <a class="link" href="s14.html#idx_id_66">V</a> <a class="link" href="s14.html#idx_id_67">W</a></p>
<div class="variablelist"><dl>
<dt>
Modified: trunk/libs/math/doc/sf_and_dist/html/index/s15.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/index/s15.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/index/s15.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -24,7 +24,7 @@
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
-<a name="id1501835"></a>Macro Index</h2></div></div></div>
+<a name="id1459128"></a>Macro Index</h2></div></div></div>
<p><a class="link" href="s15.html#idx_id_70">B</a> <a class="link" href="s15.html#idx_id_74">F</a></p>
<div class="variablelist"><dl>
<dt>
Modified: trunk/libs/math/doc/sf_and_dist/html/index/s16.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/index/s16.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/index/s16.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -23,7 +23,7 @@
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
-<a name="id1502998"></a>Index</h2></div></div></div>
+<a name="id1461656"></a>Index</h2></div></div></div>
<p><a class="link" href="s16.html#idx_id_92">A</a> <a class="link" href="s16.html#idx_id_93">B</a> <a class="link" href="s16.html#idx_id_94">C</a> <a class="link" href="s16.html#idx_id_95">D</a> <a class="link" href="s16.html#idx_id_96">E</a> <a class="link" href="s16.html#idx_id_97">F</a> <a class="link" href="s16.html#idx_id_98">G</a> <a class="link" href="s16.html#idx_id_99">H</a> <a class="link" href="s16.html#idx_id_100">I</a> <a class="link" href="s16.html#idx_id_101">K</a> <a class="link" href="s16.html#idx_id_102">L</a> <a class="link" href="s16.html#idx_id_103">M</a> <a class="link" href="s16.html#idx_id_104">N</a> <a class="link" href="s16.html#idx_id_105">O</a> <a class="link" href="s16.html#idx_id_106">P</a> <a class="link" href="s16.html#idx_id_107">Q</a> <a class="link" href="s16.html#idx_id_108">R</a> <a class="link" href="s16.html#idx_id_109">S</a> <a class="link" href="s16.html#idx_id_110">T</a> <a class="link" href="s16.html#idx_id_111">U</a> <a class="link" href="s16.html#idx_id_112">V</a
> <a class="link" href="s16.html#idx_id_113">W</a> <a class="link" href="s16.html#idx_id_114">Z</a></p>
<div class="variablelist"><dl>
<dt>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -32,9 +32,9 @@
of each function or distribution. The notes here are of a more general nature,
and reflect more the general implementation philosophy used.
</p>
-<a name="math_toolkit.backgrounders.implementation.implemention_philosophy"></a><h5>
-<a name="math_toolkit.backgrounders.implementation.implemention_philosophy-heading"></a>
- <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.implemention_philosophy">Implemention
+<h5>
+<a name="math_toolkit.backgrounders.implementation.h0"></a>
+ <span><a name="math_toolkit.backgrounders.implementation.implemention_philosophy"></a></span><a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.implemention_philosophy">Implemention
philosophy</a>
</h5>
<p>
@@ -84,9 +84,9 @@
<p>
These could still provide sufficient accuracy for some speed-critical applications.
</p>
-<a name="math_toolkit.backgrounders.implementation.accuracy_and_representation_of_test_values"></a><h5>
-<a name="math_toolkit.backgrounders.implementation.accuracy_and_representation_of_test_values-heading"></a>
- <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.accuracy_and_representation_of_test_values">Accuracy
+<h5>
+<a name="math_toolkit.backgrounders.implementation.h1"></a>
+ <span><a name="math_toolkit.backgrounders.implementation.accuracy_and_representation_of_test_values"></a></span><a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.accuracy_and_representation_of_test_values">Accuracy
and Representation of Test Values</a>
</h5>
<p>
@@ -129,9 +129,9 @@
a power of two (in order to ensure that the result is an exactly representable
binary value).
</p>
-<a name="math_toolkit.backgrounders.implementation.tolerance_of_tests"></a><h5>
-<a name="math_toolkit.backgrounders.implementation.tolerance_of_tests-heading"></a>
- <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.tolerance_of_tests">Tolerance
+<h5>
+<a name="math_toolkit.backgrounders.implementation.h2"></a>
+ <span><a name="math_toolkit.backgrounders.implementation.tolerance_of_tests"></a></span><a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.tolerance_of_tests">Tolerance
of Tests</a>
</h5>
<p>
@@ -155,9 +155,9 @@
fail on other systems where long double is more accurate than double. Check
first that the suffix L is present, and then that the tolerance is big enough.
</p>
-<a name="math_toolkit.backgrounders.implementation.handling_unsuitable_arguments"></a><h5>
-<a name="math_toolkit.backgrounders.implementation.handling_unsuitable_arguments-heading"></a>
- <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.handling_unsuitable_arguments">Handling
+<h5>
+<a name="math_toolkit.backgrounders.implementation.h3"></a>
+ <span><a name="math_toolkit.backgrounders.implementation.handling_unsuitable_arguments"></a></span><a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.handling_unsuitable_arguments">Handling
Unsuitable Arguments</a>
</h5>
<p>
@@ -223,9 +223,9 @@
done for most examples.
</p></td></tr>
</table></div>
-<a name="math_toolkit.backgrounders.implementation.handling_of_functions_that_are_not_mathematically_defined"></a><h5>
-<a name="math_toolkit.backgrounders.implementation.handling_of_functions_that_are_not_mathematically_defined-heading"></a>
- <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.handling_of_functions_that_are_not_mathematically_defined">Handling
+<h5>
+<a name="math_toolkit.backgrounders.implementation.h4"></a>
+ <span><a name="math_toolkit.backgrounders.implementation.handling_of_functions_that_are_not_mathematically_defined"></a></span><a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.handling_of_functions_that_are_not_mathematically_defined">Handling
of Functions that are Not Mathematically defined</a>
</h5>
<p>
@@ -257,9 +257,9 @@
domain error occurs. Catching exceptions is therefore strongly recommended.
</p></td></tr>
</table></div>
-<a name="math_toolkit.backgrounders.implementation.median_of_distributions"></a><h5>
-<a name="math_toolkit.backgrounders.implementation.median_of_distributions-heading"></a>
- <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.median_of_distributions">Median
+<h5>
+<a name="math_toolkit.backgrounders.implementation.h5"></a>
+ <span><a name="math_toolkit.backgrounders.implementation.median_of_distributions"></a></span><a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.median_of_distributions">Median
of distributions</a>
</h5>
<p>
@@ -292,9 +292,9 @@
<a href="http://documents.wolfram.com/v5/TheMathematicaBook/AdvancedMathematicsInMathematica/NumericalOperationsOnData/3.8.1.html" target="_top">Mathematica
Basic Statistics.</a> give more detail, in particular for discrete distributions.
</p>
-<a name="math_toolkit.backgrounders.implementation.handling_of_floating_point_infinity"></a><h5>
-<a name="math_toolkit.backgrounders.implementation.handling_of_floating_point_infinity-heading"></a>
- <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.handling_of_floating_point_infinity">Handling
+<h5>
+<a name="math_toolkit.backgrounders.implementation.h6"></a>
+ <span><a name="math_toolkit.backgrounders.implementation.handling_of_floating_point_infinity"></a></span><a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.handling_of_floating_point_infinity">Handling
of Floating-Point Infinity</a>
</h5>
<p>
@@ -336,9 +336,9 @@
What happens at (and near), poles can be controlled through <a class="link" href="../policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">error
handling policies</a>.
</p>
-<a name="math_toolkit.backgrounders.implementation.scale__shape_and_location"></a><h5>
-<a name="math_toolkit.backgrounders.implementation.scale__shape_and_location-heading"></a>
- <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.scale__shape_and_location">Scale,
+<h5>
+<a name="math_toolkit.backgrounders.implementation.h7"></a>
+ <span><a name="math_toolkit.backgrounders.implementation.scale__shape_and_location"></a></span><a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.scale__shape_and_location">Scale,
Shape and Location</a>
</h5>
<p>
@@ -363,9 +363,9 @@
for too many distributions to be generally applicable. Because they are non-member
functions, they can be added if required.
</p>
-<a name="math_toolkit.backgrounders.implementation.notes_on_implementation_of_specific_functions__amp__distributions"></a><h5>
-<a name="math_toolkit.backgrounders.implementation.notes_on_implementation_of_specific_functions__amp__distributions-heading"></a>
- <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.notes_on_implementation_of_specific_functions__amp__distributions">Notes
+<h5>
+<a name="math_toolkit.backgrounders.implementation.h8"></a>
+ <span><a name="math_toolkit.backgrounders.implementation.notes_on_implementation_of_specific_functions__amp__distributions"></a></span><a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.notes_on_implementation_of_specific_functions__amp__distributions">Notes
on Implementation of Specific Functions & Distributions</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
@@ -375,9 +375,9 @@
as a approximation for the normal distribution, the most common usage,
lower = -1, mode = 0 and upper = 1 would be more suitable.
</li></ul></div>
-<a name="math_toolkit.backgrounders.implementation.rational_approximations_used"></a><h5>
-<a name="math_toolkit.backgrounders.implementation.rational_approximations_used-heading"></a>
- <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.rational_approximations_used">Rational
+<h5>
+<a name="math_toolkit.backgrounders.implementation.h9"></a>
+ <span><a name="math_toolkit.backgrounders.implementation.rational_approximations_used"></a></span><a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.rational_approximations_used">Rational
Approximations Used</a>
</h5>
<p>
@@ -418,9 +418,9 @@
still need to be accurately calculated, even if they can be in error compared
to the "true" minimax solution.
</p>
-<a name="math_toolkit.backgrounders.implementation.representation_of_mathematical_constants"></a><h5>
-<a name="math_toolkit.backgrounders.implementation.representation_of_mathematical_constants-heading"></a>
- <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.representation_of_mathematical_constants">Representation
+<h5>
+<a name="math_toolkit.backgrounders.implementation.h10"></a>
+ <span><a name="math_toolkit.backgrounders.implementation.representation_of_mathematical_constants"></a></span><a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.representation_of_mathematical_constants">Representation
of Mathematical Constants</a>
</h5>
<p>
@@ -479,9 +479,9 @@
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">;</span> <span class="comment">// Context does not allow for disambiguation of overloaded function</span>
<span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">();</span> <span class="comment">// Context does not allow for disambiguation of overloaded function</span>
</pre>
-<a name="math_toolkit.backgrounders.implementation.thread_safety"></a><h5>
-<a name="math_toolkit.backgrounders.implementation.thread_safety-heading"></a>
- <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.thread_safety">Thread
+<h5>
+<a name="math_toolkit.backgrounders.implementation.h11"></a>
+ <span><a name="math_toolkit.backgrounders.implementation.thread_safety"></a></span><a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.thread_safety">Thread
safety</a>
</h5>
<p>
@@ -504,9 +504,9 @@
next C++ std revision, so hopefully all compilers will be required to do
the right thing here at some point.
</p>
-<a name="math_toolkit.backgrounders.implementation.sources_of_test_data"></a><h5>
-<a name="math_toolkit.backgrounders.implementation.sources_of_test_data-heading"></a>
- <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.sources_of_test_data">Sources
+<h5>
+<a name="math_toolkit.backgrounders.implementation.h12"></a>
+ <span><a name="math_toolkit.backgrounders.implementation.sources_of_test_data"></a></span><a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.sources_of_test_data">Sources
of Test Data</a>
</h5>
<p>
@@ -545,9 +545,9 @@
unfortunately it appears to suffer from very poor accuracy in areas where
the underlying special function is known to be difficult to implement.
</p>
-<a name="math_toolkit.backgrounders.implementation.creating_and_managing_the_equations"></a><h5>
-<a name="math_toolkit.backgrounders.implementation.creating_and_managing_the_equations-heading"></a>
- <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.creating_and_managing_the_equations">Creating
+<h5>
+<a name="math_toolkit.backgrounders.implementation.h13"></a>
+ <span><a name="math_toolkit.backgrounders.implementation.creating_and_managing_the_equations"></a></span><a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.creating_and_managing_the_equations">Creating
and Managing the Equations</a>
</h5>
<p>
@@ -730,9 +730,9 @@
MathML is not currently present in the Docbook output, or in the generated
HTML: this needs further investigation.
</p>
-<a name="math_toolkit.backgrounders.implementation.producing_graphs"></a><h5>
-<a name="math_toolkit.backgrounders.implementation.producing_graphs-heading"></a>
- <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.producing_graphs">Producing
+<h5>
+<a name="math_toolkit.backgrounders.implementation.h14"></a>
+ <span><a name="math_toolkit.backgrounders.implementation.producing_graphs"></a></span><a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.producing_graphs">Producing
Graphs</a>
</h5>
<p>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -26,9 +26,9 @@
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.backgrounders.lanczos"></a><a class="link" href="lanczos.html" title="The Lanczos Approximation">The Lanczos Approximation</a>
</h3></div></div></div>
-<a name="math_toolkit.backgrounders.lanczos.motivation"></a><h5>
-<a name="math_toolkit.backgrounders.lanczos.motivation-heading"></a>
- <a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.motivation">Motivation</a>
+<h5>
+<a name="math_toolkit.backgrounders.lanczos.h0"></a>
+ <span><a name="math_toolkit.backgrounders.lanczos.motivation"></a></span><a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.motivation">Motivation</a>
</h5>
<p>
<span class="emphasis"><em>Why base gamma and gamma-like functions on the Lanczos approximation?</em></span>
@@ -98,10 +98,9 @@
use similar analytic combinations of power terms, to combine gamma and beta
functions divided by large powers into single (simpler) expressions.
</p>
-<a name="math_toolkit.backgrounders.lanczos.the_approximation"></a><h5>
-<a name="math_toolkit.backgrounders.lanczos.the_approximation-heading"></a>
- <a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.the_approximation">The
- Approximation</a>
+<h5>
+<a name="math_toolkit.backgrounders.lanczos.h1"></a>
+ <span><a name="math_toolkit.backgrounders.lanczos.the_approximation"></a></span><a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.the_approximation">The Approximation</a>
</h5>
<p>
The Lanczos Approximation to the Gamma Function is given by:
@@ -160,9 +159,9 @@
so take care when referring to the literature in this field.
</p></td></tr>
</table></div>
-<a name="math_toolkit.backgrounders.lanczos.computing_the_coefficients"></a><h5>
-<a name="math_toolkit.backgrounders.lanczos.computing_the_coefficients-heading"></a>
- <a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.computing_the_coefficients">Computing
+<h5>
+<a name="math_toolkit.backgrounders.lanczos.h2"></a>
+ <span><a name="math_toolkit.backgrounders.lanczos.computing_the_coefficients"></a></span><a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.computing_the_coefficients">Computing
the Coefficients</a>
</h5>
<p>
@@ -204,9 +203,9 @@
on <span class="emphasis"><em>N</em></span>, this product should be computed first, and then
multiplied by <span class="emphasis"><em>F</em></span> as the last step.
</p>
-<a name="math_toolkit.backgrounders.lanczos.choosing_the_right_parameters"></a><h5>
-<a name="math_toolkit.backgrounders.lanczos.choosing_the_right_parameters-heading"></a>
- <a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.choosing_the_right_parameters">Choosing
+<h5>
+<a name="math_toolkit.backgrounders.lanczos.h3"></a>
+ <span><a name="math_toolkit.backgrounders.lanczos.choosing_the_right_parameters"></a></span><a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.choosing_the_right_parameters">Choosing
the Right Parameters</a>
</h5>
<p>
@@ -534,9 +533,9 @@
an inexact value: this reduces accuracy in the common case that the input
is exact, and so isn't used for the gamma function.
</p>
-<a name="math_toolkit.backgrounders.lanczos.references"></a><h5>
-<a name="math_toolkit.backgrounders.lanczos.references-heading"></a>
- <a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.references">References</a>
+<h5>
+<a name="math_toolkit.backgrounders.lanczos.h4"></a>
+ <span><a name="math_toolkit.backgrounders.lanczos.references"></a></span><a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.references">References</a>
</h5>
<div class="orderedlist"><ol class="orderedlist" type="1">
<li class="listitem">
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -26,9 +26,9 @@
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.backgrounders.refs"></a><a class="link" href="refs.html" title="References">References</a>
</h3></div></div></div>
-<a name="math_toolkit.backgrounders.refs.general_references"></a><h5>
-<a name="math_toolkit.backgrounders.refs.general_references-heading"></a>
- <a class="link" href="refs.html#math_toolkit.backgrounders.refs.general_references">General
+<h5>
+<a name="math_toolkit.backgrounders.refs.h0"></a>
+ <span><a name="math_toolkit.backgrounders.refs.general_references"></a></span><a class="link" href="refs.html#math_toolkit.backgrounders.refs.general_references">General
references</a>
</h5>
<p>
@@ -97,9 +97,9 @@
03-0097, A Proposal to Add Mathematical Special Functions to the C++ Standard
Library (version 2), Walter E. Brown</a>
</p>
-<a name="math_toolkit.backgrounders.refs.calculators"></a><h5>
-<a name="math_toolkit.backgrounders.refs.calculators-heading"></a>
- <a class="link" href="refs.html#math_toolkit.backgrounders.refs.calculators">Calculators</a>
+<h5>
+<a name="math_toolkit.backgrounders.refs.h1"></a>
+ <span><a name="math_toolkit.backgrounders.refs.calculators"></a></span><a class="link" href="refs.html#math_toolkit.backgrounders.refs.calculators">Calculators</a>
</h5>
<p>
We found (and used to create cross-check spot values - as far as their accuracy
@@ -119,9 +119,10 @@
<a href="http://www.adsciengineering.com/bpdcalc/" target="_top">http://www.adsciengineering.com/bpdcalc/>
Binomial Probability Distribution Calculator.
</p>
-<a name="math_toolkit.backgrounders.refs.other_libraries"></a><h5>
-<a name="math_toolkit.backgrounders.refs.other_libraries-heading"></a>
- <a class="link" href="refs.html#math_toolkit.backgrounders.refs.other_libraries">Other Libraries</a>
+<h5>
+<a name="math_toolkit.backgrounders.refs.h2"></a>
+ <span><a name="math_toolkit.backgrounders.refs.other_libraries"></a></span><a class="link" href="refs.html#math_toolkit.backgrounders.refs.other_libraries">Other
+ Libraries</a>
</h5>
<p>
<a href="http://www.moshier.net/#Cephes" target="_top">Cephes library</a> by Shephen
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -77,9 +77,9 @@
errors differ by a factor of 2, can actually be accurate to the same number
of binary digits. You have been warned!
</p>
-<a name="zero_error"></a><a name="math_toolkit.backgrounders.relative_error.the_impossibility_of_zero_error"></a><h5>
-<a name="math_toolkit.backgrounders.relative_error.the_impossibility_of_zero_error-heading"></a>
- <a class="link" href="relative_error.html#math_toolkit.backgrounders.relative_error.the_impossibility_of_zero_error">The
+<a name="zero_error"></a><h5>
+<a name="math_toolkit.backgrounders.relative_error.h0"></a>
+ <span><a name="math_toolkit.backgrounders.relative_error.the_impossibility_of_zero_error"></a></span><a class="link" href="relative_error.html#math_toolkit.backgrounders.relative_error.the_impossibility_of_zero_error">The
Impossibility of Zero Error</a>
</h5>
<p>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -93,10 +93,10 @@
<span class="emphasis"><em>Unfortunately we don't know where the extrema of the error function
are located!</em></span>
</p>
-<a name="math_toolkit.backgrounders.remez.the_remez_method"></a><h5>
-<a name="math_toolkit.backgrounders.remez.the_remez_method-heading"></a>
- <a class="link" href="remez.html#math_toolkit.backgrounders.remez.the_remez_method">The Remez
- Method</a>
+<h5>
+<a name="math_toolkit.backgrounders.remez.h0"></a>
+ <span><a name="math_toolkit.backgrounders.remez.the_remez_method"></a></span><a class="link" href="remez.html#math_toolkit.backgrounders.remez.the_remez_method">The
+ Remez Method</a>
</h5>
<p>
The Remez method is an iterative technique which, given a broad range of
@@ -173,10 +173,10 @@
</p>
</td></tr>
</table></div>
-<a name="math_toolkit.backgrounders.remez.remez_step_1"></a><h5>
-<a name="math_toolkit.backgrounders.remez.remez_step_1-heading"></a>
- <a class="link" href="remez.html#math_toolkit.backgrounders.remez.remez_step_1">Remez Step
- 1</a>
+<h5>
+<a name="math_toolkit.backgrounders.remez.h1"></a>
+ <span><a name="math_toolkit.backgrounders.remez.remez_step_1"></a></span><a class="link" href="remez.html#math_toolkit.backgrounders.remez.remez_step_1">Remez
+ Step 1</a>
</h5>
<p>
The first step in the Remez method, given our current set of N+2 Chebyshev
@@ -204,10 +204,10 @@
not located at the extrema, but the maximum relative error has now dropped
to 5.6x10<sup>-4</sup>.
</p>
-<a name="math_toolkit.backgrounders.remez.remez_step_2"></a><h5>
-<a name="math_toolkit.backgrounders.remez.remez_step_2-heading"></a>
- <a class="link" href="remez.html#math_toolkit.backgrounders.remez.remez_step_2">Remez Step
- 2</a>
+<h5>
+<a name="math_toolkit.backgrounders.remez.h2"></a>
+ <span><a name="math_toolkit.backgrounders.remez.remez_step_2"></a></span><a class="link" href="remez.html#math_toolkit.backgrounders.remez.remez_step_2">Remez
+ Step 2</a>
</h5>
<p>
The second step is to locate the extrema of the new approximation, which
@@ -233,9 +233,9 @@
<p>
In our example we perform multi-point exchange.
</p>
-<a name="math_toolkit.backgrounders.remez.iteration"></a><h5>
-<a name="math_toolkit.backgrounders.remez.iteration-heading"></a>
- <a class="link" href="remez.html#math_toolkit.backgrounders.remez.iteration">Iteration</a>
+<h5>
+<a name="math_toolkit.backgrounders.remez.h3"></a>
+ <span><a name="math_toolkit.backgrounders.remez.iteration"></a></span><a class="link" href="remez.html#math_toolkit.backgrounders.remez.iteration">Iteration</a>
</h5>
<p>
The Remez method then performs steps 1 and 2 above iteratively until the
@@ -249,9 +249,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../graphs/remez-4.png" alt="remez-4"></span>
</p>
-<a name="math_toolkit.backgrounders.remez.rational_approximations"></a><h5>
-<a name="math_toolkit.backgrounders.remez.rational_approximations-heading"></a>
- <a class="link" href="remez.html#math_toolkit.backgrounders.remez.rational_approximations">Rational
+<h5>
+<a name="math_toolkit.backgrounders.remez.h4"></a>
+ <span><a name="math_toolkit.backgrounders.remez.rational_approximations"></a></span><a class="link" href="remez.html#math_toolkit.backgrounders.remez.rational_approximations">Rational
Approximations</a>
</h5>
<p>
@@ -298,9 +298,9 @@
error drops to 8.7x10<sup>-5</sup>. That's a 5 fold increase in accuracy, for the same
number of terms overall.
</p>
-<a name="math_toolkit.backgrounders.remez.practical_considerations"></a><h5>
-<a name="math_toolkit.backgrounders.remez.practical_considerations-heading"></a>
- <a class="link" href="remez.html#math_toolkit.backgrounders.remez.practical_considerations">Practical
+<h5>
+<a name="math_toolkit.backgrounders.remez.h5"></a>
+ <span><a name="math_toolkit.backgrounders.remez.practical_considerations"></a></span><a class="link" href="remez.html#math_toolkit.backgrounders.remez.practical_considerations">Practical
Considerations</a>
</h5>
<p>
@@ -406,10 +406,10 @@
It's clearly still not ideal, but it is only a few percent away from our
desired minimax solution (5x10<sup>-4</sup>).
</p>
-<a name="math_toolkit.backgrounders.remez.remez_method_checklist"></a><h5>
-<a name="math_toolkit.backgrounders.remez.remez_method_checklist-heading"></a>
- <a class="link" href="remez.html#math_toolkit.backgrounders.remez.remez_method_checklist">Remez
- Method Checklist</a>
+<h5>
+<a name="math_toolkit.backgrounders.remez.h6"></a>
+ <span><a name="math_toolkit.backgrounders.remez.remez_method_checklist"></a></span><a class="link" href="remez.html#math_toolkit.backgrounders.remez.remez_method_checklist">Remez Method
+ Checklist</a>
</h5>
<p>
The following lists some of the things to check if the Remez method goes
@@ -460,9 +460,9 @@
over, say [0, b], for some smallish value <span class="emphasis"><em>b</em></span>.
</li>
</ul></div>
-<a name="math_toolkit.backgrounders.remez.references"></a><h5>
-<a name="math_toolkit.backgrounders.remez.references-heading"></a>
- <a class="link" href="remez.html#math_toolkit.backgrounders.remez.references">References</a>
+<h5>
+<a name="math_toolkit.backgrounders.remez.h7"></a>
+ <span><a name="math_toolkit.backgrounders.remez.references"></a></span><a class="link" href="remez.html#math_toolkit.backgrounders.remez.references">References</a>
</h5>
<p>
The original references for the Remez Method and it's extension to rational
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -27,9 +27,9 @@
<a name="math_toolkit.dist.dist_ref.dist_algorithms"></a><a class="link" href="dist_algorithms.html" title="Distribution Algorithms">Distribution
Algorithms</a>
</h4></div></div></div>
-<a name="math_toolkit.dist.dist_ref.dist_algorithms.finding_the_location_and_scale_for_normal_and_similar_distributions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dist_algorithms.finding_the_location_and_scale_for_normal_and_similar_distributions-heading"></a>
- <a class="link" href="dist_algorithms.html#math_toolkit.dist.dist_ref.dist_algorithms.finding_the_location_and_scale_for_normal_and_similar_distributions">Finding
+<h5>
+<a name="math_toolkit.dist.dist_ref.dist_algorithms.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dist_algorithms.finding_the_location_and_scale_for_normal_and_similar_distributions"></a></span><a class="link" href="dist_algorithms.html#math_toolkit.dist.dist_ref.dist_algorithms.finding_the_location_and_scale_for_normal_and_similar_distributions">Finding
the Location and Scale for Normal and similar distributions</a>
</h5>
<p>
@@ -49,13 +49,12 @@
<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">;</span> <span class="comment">// May be needed by users defining their own policies.</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">complement</span><span class="special">;</span> <span class="comment">// Will be needed by users who want to use complements.</span>
</pre>
-<a name="math_toolkit.dist.dist_ref.dist_algorithms.find_location_function"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dist_algorithms.find_location_function-heading"></a>
- <a class="link" href="dist_algorithms.html#math_toolkit.dist.dist_ref.dist_algorithms.find_location_function">find_location
+<h5>
+<a name="math_toolkit.dist.dist_ref.dist_algorithms.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dist_algorithms.find_location_function"></a></span><a class="link" href="dist_algorithms.html#math_toolkit.dist.dist_ref.dist_algorithms.find_location_function">find_location
function</a>
</h5>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">find_location</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
@@ -79,18 +78,17 @@
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
-<a name="math_toolkit.dist.dist_ref.dist_algorithms.find_scale_function"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dist_algorithms.find_scale_function-heading"></a>
- <a class="link" href="dist_algorithms.html#math_toolkit.dist.dist_ref.dist_algorithms.find_scale_function">find_scale
+<h5>
+<a name="math_toolkit.dist.dist_ref.dist_algorithms.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dist_algorithms.find_scale_function"></a></span><a class="link" href="dist_algorithms.html#math_toolkit.dist.dist_ref.dist_algorithms.find_scale_function">find_scale
function</a>
</h5>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">find_scale</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Dist</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span>
<span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">find_scale</span><span class="special">(</span> <span class="comment">// For example, normal mean.</span>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,16 +28,15 @@
Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">bernoulli</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
- <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+ <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">bernoulli_distribution</span><span class="special">;</span>
-
+
<span class="keyword">typedef</span> <span class="identifier">bernoulli_distribution</span><span class="special"><></span> <span class="identifier">bernoulli</span><span class="special">;</span>
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">></span>
@@ -51,7 +50,7 @@
<span class="comment">// Accessor function.</span>
<span class="identifier">RealType</span> <span class="identifier">success_fraction</span><span class="special">()</span> <span class="keyword">const</span>
<span class="comment">// Probability of success (as a fraction).</span>
- <span class="special">};</span>
+ <span class="special">};</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<p>
@@ -86,9 +85,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/bernoulli_cdf.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.member_functions-heading"></a>
- <a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.member_functions"></a></span><a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">bernoulli_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
@@ -102,9 +101,9 @@
<p>
Returns the <span class="emphasis"><em>success_fraction</em></span> parameter of this distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.non_member_accessors-heading"></a>
- <a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.non_member_accessors"></a></span><a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -127,17 +126,17 @@
Outside this range, functions are undefined, or may throw domain_error
exception and make an error message available.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.accuracy-heading"></a>
- <a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.accuracy"></a></span><a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.accuracy">Accuracy</a>
</h5>
<p>
The Bernoulli distribution is implemented with simple arithmetic operators
and so should have errors within an epsilon or two.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.implementation-heading"></a>
- <a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.implementation"></a></span><a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.implementation">Implementation</a>
</h5>
<p>
In the following table <span class="emphasis"><em>p</em></span> is the probability of success
@@ -326,9 +325,9 @@
</tr>
</tbody>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.references"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.references-heading"></a>
- <a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.references">References</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.references"></a></span><a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.references">References</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,14 +28,13 @@
Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">beta</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
- <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+ <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">beta_distribution</span><span class="special">;</span>
@@ -51,28 +50,28 @@
<span class="keyword">typedef</span> <span class="identifier">Policy</span> <span class="identifier">policy_type</span><span class="special">;</span>
<span class="comment">// Constructor from two shape parameters, alpha & beta:</span>
<span class="identifier">beta_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">b</span><span class="special">);</span>
-
+
<span class="comment">// Parameter accessors:</span>
<span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">RealType</span> <span class="identifier">beta</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
-
+
<span class="comment">// Parameter estimators of alpha or beta from mean and variance.</span>
<span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_alpha</span><span class="special">(</span>
<span class="identifier">RealType</span> <span class="identifier">mean</span><span class="special">,</span> <span class="comment">// Expected value of mean.</span>
<span class="identifier">RealType</span> <span class="identifier">variance</span><span class="special">);</span> <span class="comment">// Expected value of variance.</span>
-
+
<span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_beta</span><span class="special">(</span>
<span class="identifier">RealType</span> <span class="identifier">mean</span><span class="special">,</span> <span class="comment">// Expected value of mean.</span>
<span class="identifier">RealType</span> <span class="identifier">variance</span><span class="special">);</span> <span class="comment">// Expected value of variance.</span>
<span class="comment">// Parameter estimators from from</span>
<span class="comment">// either alpha or beta, and x and probability.</span>
-
+
<span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_alpha</span><span class="special">(</span>
<span class="identifier">RealType</span> <span class="identifier">beta</span><span class="special">,</span> <span class="comment">// from beta.</span>
<span class="identifier">RealType</span> <span class="identifier">x</span><span class="special">,</span> <span class="comment">// x.</span>
<span class="identifier">RealType</span> <span class="identifier">probability</span><span class="special">);</span> <span class="comment">// cdf</span>
-
+
<span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_beta</span><span class="special">(</span>
<span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">,</span> <span class="comment">// alpha.</span>
<span class="identifier">RealType</span> <span class="identifier">x</span><span class="special">,</span> <span class="comment">// probability x.</span>
@@ -131,14 +130,14 @@
β, then the shape is asymmetric and could be approximated by a triangle
whose apex is away from the centre (where x = half).
</p>
-<a name="math_toolkit.dist.dist_ref.dists.beta_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.beta_dist.member_functions-heading"></a>
- <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.beta_dist.member_functions"></a></span><a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.member_functions">Member
Functions</a>
</h5>
-<a name="math_toolkit.dist.dist_ref.dists.beta_dist.constructor"></a><h6>
-<a name="math_toolkit.dist.dist_ref.dists.beta_dist.constructor-heading"></a>
- <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.constructor">Constructor</a>
+<h6>
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.beta_dist.constructor"></a></span><a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.constructor">Constructor</a>
</h6>
<pre class="programlisting"><span class="identifier">beta_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">beta</span><span class="special">);</span>
</pre>
@@ -163,9 +162,9 @@
Constructs a the beta distribution with alpha=2 and beta=5 (shown in
yellow in the graph above).
</p>
-<a name="math_toolkit.dist.dist_ref.dists.beta_dist.parameter_accessors"></a><h6>
-<a name="math_toolkit.dist.dist_ref.dists.beta_dist.parameter_accessors-heading"></a>
- <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.parameter_accessors">Parameter
+<h6>
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.beta_dist.parameter_accessors"></a></span><a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.parameter_accessors">Parameter
Accessors</a>
</h6>
<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
@@ -187,9 +186,9 @@
<span class="identifier">assert</span><span class="special">(</span><span class="identifier">mybeta</span><span class="special">.</span><span class="identifier">alpha</span><span class="special">()</span> <span class="special">==</span> <span class="number">2.</span><span class="special">);</span> <span class="comment">// mybeta.alpha() returns 2</span>
<span class="identifier">assert</span><span class="special">(</span><span class="identifier">mybeta</span><span class="special">.</span><span class="identifier">beta</span><span class="special">()</span> <span class="special">==</span> <span class="number">5.</span><span class="special">);</span> <span class="comment">// mybeta.beta() returns 5</span>
</pre>
-<a name="math_toolkit.dist.dist_ref.dists.beta_dist.parameter_estimators"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.beta_dist.parameter_estimators-heading"></a>
- <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.parameter_estimators">Parameter
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.beta_dist.parameter_estimators"></a></span><a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.parameter_estimators">Parameter
Estimators</a>
</h5>
<p>
@@ -240,9 +239,9 @@
<p>
Returns the value of β   that gives: <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">beta_distribution</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">>(</span><span class="identifier">alpha</span><span class="special">,</span> <span class="identifier">beta</span><span class="special">),</span> <span class="identifier">x</span><span class="special">)</span> <span class="special">==</span> <span class="identifier">probability</span></code>.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.beta_dist.non_member_accessor_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.beta_dist.non_member_accessor_functions-heading"></a>
- <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.non_member_accessor_functions">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.beta_dist.non_member_accessor_functions"></a></span><a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.non_member_accessor_functions">Non-member
Accessor Functions</a>
</h5>
<p>
@@ -262,9 +261,9 @@
at <a href="http://mathworld.wolfram.com/BetaDistribution.html" target="_top">Wolfram
Mathworld</a>.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.beta_dist.applications"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.beta_dist.applications-heading"></a>
- <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.applications">Applications</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist.h5"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.beta_dist.applications"></a></span><a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.applications">Applications</a>
</h5>
<p>
The beta distribution can be used to model events constrained to take
@@ -275,9 +274,9 @@
It is also widely used in <a href="http://en.wikipedia.org/wiki/Bayesian_inference" target="_top">Bayesian
statistical inference</a>.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.beta_dist.related_distributions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.beta_dist.related_distributions-heading"></a>
- <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.related_distributions">Related
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist.h6"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.beta_dist.related_distributions"></a></span><a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.related_distributions">Related
distributions</a>
</h5>
<p>
@@ -302,9 +301,9 @@
are less than x, a probability given by summing over the <a class="link" href="binomial_dist.html" title="Binomial Distribution">Binomial
Distribution</a> with its p parameter set to x.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.beta_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.beta_dist.accuracy-heading"></a>
- <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist.h7"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.beta_dist.accuracy"></a></span><a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.accuracy">Accuracy</a>
</h5>
<p>
This distribution is implemented using the <a class="link" href="../../../special/sf_beta/beta_function.html" title="Beta">beta
@@ -314,9 +313,9 @@
and <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>;
please refer to these functions for information on accuracy.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.beta_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.beta_dist.implementation-heading"></a>
- <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist.h8"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.beta_dist.implementation"></a></span><a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.implementation">Implementation</a>
</h5>
<p>
In the following table <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span>
@@ -593,9 +592,9 @@
</tr>
</tbody>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.beta_dist.references"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.beta_dist.references-heading"></a>
- <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.references">References</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist.h9"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.beta_dist.references"></a></span><a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.references">References</a>
</h5>
<p>
<a href="http://en.wikipedia.org/wiki/Beta_distribution" target="_top">Wikipedia
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,14 +28,13 @@
Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">binomial_distribution</span><span class="special">;</span>
@@ -47,35 +46,35 @@
<span class="keyword">public</span><span class="special">:</span>
<span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">Policy</span> <span class="identifier">policy_type</span><span class="special">;</span>
-
+
<span class="keyword">static</span> <span class="keyword">const</span> <span class="emphasis"><em>unspecified-type</em></span> <span class="identifier">clopper_pearson_exact_interval</span><span class="special">;</span>
<span class="keyword">static</span> <span class="keyword">const</span> <span class="emphasis"><em>unspecified-type</em></span> <span class="identifier">jeffreys_prior_interval</span><span class="special">;</span>
-
+
<span class="comment">// construct:</span>
<span class="identifier">binomial_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
-
+
<span class="comment">// parameter access::</span>
<span class="identifier">RealType</span> <span class="identifier">success_fraction</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
-
+
<span class="comment">// Bounds on success fraction:</span>
<span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_lower_bound_on_p</span><span class="special">(</span>
- <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span>
+ <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">probability</span><span class="special">,</span>
<span class="emphasis"><em>unspecified-type</em></span> <span class="identifier">method</span> <span class="special">=</span> <span class="identifier">clopper_pearson_exact_interval</span><span class="special">);</span>
<span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_upper_bound_on_p</span><span class="special">(</span>
- <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span>
+ <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">probability</span><span class="special">,</span>
<span class="emphasis"><em>unspecified-type</em></span> <span class="identifier">method</span> <span class="special">=</span> <span class="identifier">clopper_pearson_exact_interval</span><span class="special">);</span>
-
+
<span class="comment">// estimate min/max number of trials:</span>
<span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_minimum_number_of_trials</span><span class="special">(</span>
<span class="identifier">RealType</span> <span class="identifier">k</span><span class="special">,</span> <span class="comment">// number of events</span>
<span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">,</span> <span class="comment">// success fraction</span>
<span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">);</span> <span class="comment">// risk level</span>
-
+
<span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_maximum_number_of_trials</span><span class="special">(</span>
<span class="identifier">RealType</span> <span class="identifier">k</span><span class="special">,</span> <span class="comment">// number of events</span>
<span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">,</span> <span class="comment">// success fraction</span>
@@ -160,14 +159,14 @@
</p>
</td></tr>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.member_functions-heading"></a>
- <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.binomial_dist.member_functions"></a></span><a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.member_functions">Member
Functions</a>
</h5>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.construct"></a><h6>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.construct-heading"></a>
- <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.construct">Construct</a>
+<h6>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.binomial_dist.construct"></a></span><a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.construct">Construct</a>
</h6>
<pre class="programlisting"><span class="identifier">binomial_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
</pre>
@@ -182,9 +181,9 @@
<span class="special">>=</span> <span class="number">0</span></code>,
otherwise calls <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.accessors"></a><h6>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.accessors-heading"></a>
- <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.accessors">Accessors</a>
+<h6>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.binomial_dist.accessors"></a></span><a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.accessors">Accessors</a>
</h6>
<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">success_fraction</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
</pre>
@@ -198,13 +197,13 @@
Returns the parameter <span class="emphasis"><em>n</em></span> from which this distribution
was constructed.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.lower_bound_on_the_success_fraction"></a><h6>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.lower_bound_on_the_success_fraction-heading"></a>
- <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.lower_bound_on_the_success_fraction">Lower
+<h6>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.binomial_dist.lower_bound_on_the_success_fraction"></a></span><a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.lower_bound_on_the_success_fraction">Lower
Bound on the Success Fraction</a>
</h6>
<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_lower_bound_on_p</span><span class="special">(</span>
- <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span>
+ <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">,</span>
<span class="emphasis"><em>unspecified-type</em></span> <span class="identifier">method</span> <span class="special">=</span> <span class="identifier">clopper_pearson_exact_interval</span><span class="special">);</span>
@@ -304,13 +303,13 @@
Clopper, C. J. and Pearson, E. S. (1934). The use of confidence or fiducial
limits illustrated in the case of the binomial. Biometrika 26 404-413.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.upper_bound_on_the_success_fraction"></a><h6>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.upper_bound_on_the_success_fraction-heading"></a>
- <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.upper_bound_on_the_success_fraction">Upper
+<h6>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.binomial_dist.upper_bound_on_the_success_fraction"></a></span><a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.upper_bound_on_the_success_fraction">Upper
Bound on the Success Fraction</a>
</h6>
<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_upper_bound_on_p</span><span class="special">(</span>
- <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span>
+ <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">,</span>
<span class="emphasis"><em>unspecified-type</em></span> <span class="identifier">method</span> <span class="special">=</span> <span class="identifier">clopper_pearson_exact_interval</span><span class="special">);</span>
@@ -382,9 +381,9 @@
</p>
</td></tr>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_number_of_trials_required_for_a_certain_number_of_successes"></a><h6>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_number_of_trials_required_for_a_certain_number_of_successes-heading"></a>
- <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_number_of_trials_required_for_a_certain_number_of_successes">Estimating
+<h6>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.h5"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_number_of_trials_required_for_a_certain_number_of_successes"></a></span><a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_number_of_trials_required_for_a_certain_number_of_successes">Estimating
the Number of Trials Required for a Certain Number of Successes</a>
</h6>
<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_minimum_number_of_trials</span><span class="special">(</span>
@@ -424,9 +423,9 @@
Returns the smallest number of trials we must conduct to be 95% sure
of seeing 10 events that occur with frequency one half.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_maximum_number_of_trials_to_ensure_no_more_than_a_certain_number_of_successes"></a><h6>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_maximum_number_of_trials_to_ensure_no_more_than_a_certain_number_of_successes-heading"></a>
- <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_maximum_number_of_trials_to_ensure_no_more_than_a_certain_number_of_successes">Estimating
+<h6>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.h6"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_maximum_number_of_trials_to_ensure_no_more_than_a_certain_number_of_successes"></a></span><a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_maximum_number_of_trials_to_ensure_no_more_than_a_certain_number_of_successes">Estimating
the Maximum Number of Trials to Ensure no more than a Certain Number
of Successes</a>
</h6>
@@ -472,9 +471,9 @@
<a class="link" href="../../stat_tut/weg/binom_eg/binom_size_eg.html" title="Estimating Sample Sizes for a Binomial Distribution.">See
Worked Example.</a>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.non_member_accessors-heading"></a>
- <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.h7"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.binomial_dist.non_member_accessors"></a></span><a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -621,17 +620,17 @@
</tbody>
</table></div>
</div>
-<br class="table-break"><a name="math_toolkit.dist.dist_ref.dists.binomial_dist.examples"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.examples-heading"></a>
- <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.examples">Examples</a>
+<br class="table-break"><h5>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.h8"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.binomial_dist.examples"></a></span><a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.examples">Examples</a>
</h5>
<p>
Various <a class="link" href="../../stat_tut/weg/binom_eg.html" title="Binomial Distribution Examples">worked
examples</a> are available illustrating the use of the binomial distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.accuracy-heading"></a>
- <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.h9"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.binomial_dist.accuracy"></a></span><a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.accuracy">Accuracy</a>
</h5>
<p>
This distribution is implemented using the incomplete beta functions
@@ -639,9 +638,9 @@
and <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>,
please refer to these functions for information on accuracy.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.implementation-heading"></a>
- <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.h10"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.binomial_dist.implementation"></a></span><a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.implementation">Implementation</a>
</h5>
<p>
In the following table <span class="emphasis"><em>p</em></span> is the probability that
@@ -708,7 +707,6 @@
Using the relation:
</p>
<p>
-
</p>
<pre xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="table-programlisting"><span class="identifier">p</span> <span class="special">=</span> <span class="identifier">I</span><span class="special">[</span><span class="identifier">sub</span> <span class="number">1</span><span class="special">-</span><span class="identifier">p</span><span class="special">](</span><span class="identifier">n</span> <span class="special">-</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">k</span> <span class="special">+</span> <span class="number">1</span><span class="special">)</span>
<span class="special">=</span> <span class="number">1</span> <span class="special">-</span> <span class="identifier">I</span><span class="special">[</span><span class="identifier">sub</span> <span class="identifier">p</span><span class="special">](</span><span class="identifier">k</span> <span class="special">+</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">n</span> <span class="special">-</span> <span class="identifier">k</span><span class="special">)</span>
@@ -883,9 +881,9 @@
</tr>
</tbody>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.references"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.references-heading"></a>
- <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.references">References</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.h11"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.binomial_dist.references"></a></span><a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.references">References</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,12 +28,11 @@
Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">cauchy</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">cauchy_distribution</span><span class="special">;</span>
@@ -47,7 +46,7 @@
<span class="keyword">typedef</span> <span class="identifier">Policy</span> <span class="identifier">policy_type</span><span class="special">;</span>
<span class="identifier">cauchy_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">location</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
-
+
<span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
<span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
<span class="special">};</span>
@@ -87,9 +86,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/cauchy_pdf2.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.member_functions-heading"></a>
- <a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.member_functions"></a></span><a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">cauchy_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">location</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
@@ -113,9 +112,9 @@
<p>
Returns the scale parameter of the distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.non_member_accessors-heading"></a>
- <a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.non_member_accessors"></a></span><a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -147,18 +146,18 @@
<p>
The domain of the random variable is [-[max_value], +[min_value]].
</p>
-<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.accuracy-heading"></a>
- <a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.accuracy"></a></span><a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.accuracy">Accuracy</a>
</h5>
<p>
The Cauchy distribution is implemented in terms of the standard library
<code class="computeroutput"><span class="identifier">tan</span></code> and <code class="computeroutput"><span class="identifier">atan</span></code> functions, and as such should
have very low error rates.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.implementation-heading"></a>
- <a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.implementation"></a></span><a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.implementation">Implementation</a>
</h5>
<p>
In the following table x<sub>0 </sub> is the location parameter of the distribution,
@@ -272,9 +271,9 @@
</tr>
</tbody>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.references"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.references-heading"></a>
- <a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.references">References</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.references"></a></span><a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.references">References</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,14 +28,13 @@
Squared Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">chi_squared</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">chi_squared_distribution</span><span class="special">;</span>
@@ -86,9 +85,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/chi_squared_pdf.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.member_functions-heading"></a>
- <a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.member_functions"></a></span><a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">chi_squared_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">v</span><span class="special">);</span>
@@ -169,9 +168,9 @@
See also section on Sample sizes required in <a href="http://www.itl.nist.gov/div898/handbook/prc/section2/prc232.htm" target="_top">the
NIST Engineering Statistics Handbook, Section 7.2.3.2</a>.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.non_member_accessors-heading"></a>
- <a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.non_member_accessors"></a></span><a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -195,25 +194,25 @@
<p>
The domain of the random variable is [0, +∞].
</p>
-<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.examples"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.examples-heading"></a>
- <a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.examples">Examples</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.examples"></a></span><a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.examples">Examples</a>
</h5>
<p>
Various <a class="link" href="../../stat_tut/weg/cs_eg.html" title="Chi Squared Distribution Examples">worked examples</a>
are available illustrating the use of the Chi Squared Distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.accuracy-heading"></a>
- <a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.accuracy"></a></span><a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.accuracy">Accuracy</a>
</h5>
<p>
The Chi-Squared distribution is implemented in terms of the <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">incomplete
gamma functions</a>: please refer to the accuracy data for those functions.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.implementation-heading"></a>
- <a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.implementation"></a></span><a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.implementation">Implementation</a>
</h5>
<p>
In the following table <span class="emphasis"><em>v</em></span> is the number of degrees
@@ -378,9 +377,9 @@
</tr>
</tbody>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.references"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.references-heading"></a>
- <a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.references">References</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.h5"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.references"></a></span><a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.references">References</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,12 +28,11 @@
Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">exponential</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">exponential_distribution</span><span class="special">;</span>
@@ -70,9 +69,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/exponential_pdf.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.exp_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.exp_dist.member_functions-heading"></a>
- <a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.exp_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.exp_dist.member_functions"></a></span><a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">exponential_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">lambda</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
@@ -90,9 +89,9 @@
<p>
Accessor function returns the lambda parameter of the distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.exp_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.exp_dist.non_member_accessors-heading"></a>
- <a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.exp_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.exp_dist.non_member_accessors"></a></span><a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -110,9 +109,9 @@
<p>
The domain of the random variable is [0, +∞].
</p>
-<a name="math_toolkit.dist.dist_ref.dists.exp_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.exp_dist.accuracy-heading"></a>
- <a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.exp_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.exp_dist.accuracy"></a></span><a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.accuracy">Accuracy</a>
</h5>
<p>
The exponential distribution is implemented in terms of the standard
@@ -121,9 +120,9 @@
and <code class="computeroutput"><span class="identifier">expm1</span></code> and as such
should have very low error rates.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.exp_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.exp_dist.implementation-heading"></a>
- <a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.exp_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.exp_dist.implementation"></a></span><a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.implementation">Implementation</a>
</h5>
<p>
In the following table λ is the parameter lambda of the distribution,
@@ -282,9 +281,9 @@
</tr>
</tbody>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.exp_dist.references"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.exp_dist.references-heading"></a>
- <a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.references">references</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.exp_dist.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.exp_dist.references"></a></span><a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.references">references</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,12 +28,11 @@
Value Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">extreme</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">extreme_value_distribution</span><span class="special">;</span>
@@ -99,9 +98,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/extreme_value_pdf2.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.member_functions-heading"></a>
- <a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.extreme_dist.member_functions"></a></span><a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">extreme_value_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">location</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
@@ -124,9 +123,9 @@
<p>
Returns the scale parameter of the distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.non_member_accessors-heading"></a>
- <a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.extreme_dist.non_member_accessors"></a></span><a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -144,18 +143,18 @@
<p>
The domain of the random parameter is [-∞, +∞].
</p>
-<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.accuracy-heading"></a>
- <a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.extreme_dist.accuracy"></a></span><a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.accuracy">Accuracy</a>
</h5>
<p>
The extreme value distribution is implemented in terms of the standard
library <code class="computeroutput"><span class="identifier">exp</span></code> and <code class="computeroutput"><span class="identifier">log</span></code> functions and as such should have
very low error rates.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.implementation-heading"></a>
- <a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.extreme_dist.implementation"></a></span><a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.implementation">Implementation</a>
</h5>
<p>
In the following table: <span class="emphasis"><em>a</em></span> is the location parameter,
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -27,14 +27,13 @@
<a name="math_toolkit.dist.dist_ref.dists.f_dist"></a><a class="link" href="f_dist.html" title="F Distribution">F Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">fisher_f</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
-
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">fisher_f_distribution</span><span class="special">;</span>
@@ -45,10 +44,10 @@
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
<span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
-
+
<span class="comment">// Construct:</span>
<span class="identifier">fisher_f_distribution</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&</span> <span class="identifier">i</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&</span> <span class="identifier">j</span><span class="special">);</span>
-
+
<span class="comment">// Accessors:</span>
<span class="identifier">RealType</span> <span class="identifier">degrees_of_freedom1</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
<span class="identifier">RealType</span> <span class="identifier">degrees_of_freedom2</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
@@ -79,9 +78,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/fisher_f_pdf.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.f_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.f_dist.member_functions-heading"></a>
- <a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.f_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.f_dist.member_functions"></a></span><a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">fisher_f_distribution</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&</span> <span class="identifier">df1</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&</span> <span class="identifier">df2</span><span class="special">);</span>
@@ -105,9 +104,9 @@
<p>
Returns the denominator degrees of freedom parameter of the distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.f_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.f_dist.non_member_accessors-heading"></a>
- <a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.f_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.f_dist.non_member_accessors"></a></span><a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -125,26 +124,26 @@
<p>
The domain of the random variable is [0, +∞].
</p>
-<a name="math_toolkit.dist.dist_ref.dists.f_dist.examples"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.f_dist.examples-heading"></a>
- <a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.examples">Examples</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.f_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.f_dist.examples"></a></span><a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.examples">Examples</a>
</h5>
<p>
Various <a class="link" href="../../stat_tut/weg/f_eg.html" title="F Distribution Examples">worked examples</a>
are available illustrating the use of the F Distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.f_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.f_dist.accuracy-heading"></a>
- <a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.f_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.f_dist.accuracy"></a></span><a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.accuracy">Accuracy</a>
</h5>
<p>
The normal distribution is implemented in terms of the <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">incomplete
beta function</a> and its <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">inverses</a>,
refer to those functions for accuracy data.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.f_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.f_dist.implementation-heading"></a>
- <a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.f_dist.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.f_dist.implementation"></a></span><a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.implementation">Implementation</a>
</h5>
<p>
In the following table <span class="emphasis"><em>v1</em></span> and <span class="emphasis"><em>v2</em></span>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,14 +28,13 @@
(and Erlang) Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
-
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">gamma_distribution</span>
<span class="special">{</span>
@@ -74,7 +73,6 @@
does not provide the typedef:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">gamma_distribution</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">gamma</span><span class="special">;</span></pre>
<p>
@@ -83,7 +81,6 @@
Instead if you want a double precision gamma distribution you can write
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">gamma_distribution</span><span class="special"><></span> <span class="identifier">my_gamma</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="number">1</span><span class="special">);</span></pre>
<p>
@@ -136,9 +133,9 @@
be no great loss of performance from using a Gamma Distribution rather
than a dedicated Erlang Distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.member_functions-heading"></a>
- <a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.gamma_dist.member_functions"></a></span><a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">gamma_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">shape</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
@@ -161,9 +158,9 @@
<p>
Returns the <span class="emphasis"><em>scale</em></span> parameter of this distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.non_member_accessors-heading"></a>
- <a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.gamma_dist.non_member_accessors"></a></span><a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -181,9 +178,9 @@
<p>
The domain of the random variable is [0,+∞].
</p>
-<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.accuracy-heading"></a>
- <a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.gamma_dist.accuracy"></a></span><a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.accuracy">Accuracy</a>
</h5>
<p>
The lognormal distribution is implemented in terms of the incomplete
@@ -193,9 +190,9 @@
and <a class="link" href="../../../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inv</a>:
refer to the accuracy data for those functions for more information.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.implementation-heading"></a>
- <a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.gamma_dist.implementation"></a></span><a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.implementation">Implementation</a>
</h5>
<p>
In the following table <span class="emphasis"><em>k</em></span> is the shape parameter
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/geometric_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/geometric_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/geometric_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,14 +28,13 @@
Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">geometric</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">geometric_distribution</span><span class="special">;</span>
@@ -49,21 +48,21 @@
<span class="keyword">typedef</span> <span class="identifier">Policy</span> <span class="identifier">policy_type</span><span class="special">;</span>
<span class="comment">// Constructor from success_fraction:</span>
<span class="identifier">geometric_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
-
+
<span class="comment">// Parameter accessors:</span>
<span class="identifier">RealType</span> <span class="identifier">success_fraction</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
-
+
<span class="comment">// Bounds on success fraction:</span>
<span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_lower_bound_on_p</span><span class="special">(</span>
- <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span>
+ <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">probability</span><span class="special">);</span> <span class="comment">// alpha</span>
<span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_upper_bound_on_p</span><span class="special">(</span>
- <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span>
+ <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">probability</span><span class="special">);</span> <span class="comment">// alpha</span>
-
+
<span class="comment">// Estimate min/max number of trials:</span>
<span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_minimum_number_of_trials</span><span class="special">(</span>
<span class="identifier">RealType</span> <span class="identifier">k</span><span class="special">,</span> <span class="comment">// Number of failures.</span>
@@ -145,9 +144,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/geometric_cdf_discrete.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.related_distributions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.related_distributions-heading"></a>
- <a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.related_distributions">Related
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.geometric_dist.related_distributions"></a></span><a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.related_distributions">Related
Distributions</a>
</h5>
<p>
@@ -205,14 +204,14 @@
</p>
</td></tr>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.member_functions-heading"></a>
- <a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.geometric_dist.member_functions"></a></span><a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.member_functions">Member
Functions</a>
</h5>
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.constructor"></a><h6>
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.constructor-heading"></a>
- <a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.constructor">Constructor</a>
+<h6>
+<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.geometric_dist.constructor"></a></span><a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.constructor">Constructor</a>
</h6>
<pre class="programlisting"><span class="identifier">geometric_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
</pre>
@@ -225,9 +224,9 @@
<span class="identifier">p</span> <span class="special"><=</span>
<span class="number">1</span></code>.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.accessors"></a><h6>
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.accessors-heading"></a>
- <a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.accessors">Accessors</a>
+<h6>
+<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.geometric_dist.accessors"></a></span><a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.accessors">Accessors</a>
</h6>
<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">success_fraction</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> <span class="comment">// successes / trials (0 <= p <= 1)</span>
</pre>
@@ -252,13 +251,13 @@
Distribution</a> and <a class="link" href="negative_binomial_dist.html" title="Negative Binomial Distribution">Negative
Binomial Distribution</a> for more discussion.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.lower_bound_on_success_fraction_parameter__emphasis_p__emphasis_"></a><h6>
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.lower_bound_on_success_fraction_parameter__emphasis_p__emphasis_-heading"></a>
- <a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.lower_bound_on_success_fraction_parameter__emphasis_p__emphasis_">Lower
+<h6>
+<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.geometric_dist.lower_bound_on_success_fraction_parameter__emphasis_p__emphasis_"></a></span><a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.lower_bound_on_success_fraction_parameter__emphasis_p__emphasis_">Lower
Bound on success_fraction Parameter <span class="emphasis"><em>p</em></span></a>
</h6>
<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_lower_bound_on_p</span><span class="special">(</span>
- <span class="identifier">RealType</span> <span class="identifier">failures</span><span class="special">,</span>
+ <span class="identifier">RealType</span> <span class="identifier">failures</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">probability</span><span class="special">)</span> <span class="comment">// (0 <= alpha <= 1), 0.05 equivalent to 95% confidence.</span>
</pre>
<p>
@@ -307,13 +306,13 @@
Discrete Distributions. Computational statistics and data analysis, 2005,
vol. 48, no3, 605-621</a>.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.upper_bound_on_success_fraction_parameter_p"></a><h6>
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.upper_bound_on_success_fraction_parameter_p-heading"></a>
- <a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.upper_bound_on_success_fraction_parameter_p">Upper
+<h6>
+<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.h5"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.geometric_dist.upper_bound_on_success_fraction_parameter_p"></a></span><a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.upper_bound_on_success_fraction_parameter_p">Upper
Bound on success_fraction Parameter p</a>
</h6>
<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_upper_bound_on_p</span><span class="special">(</span>
- <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span>
+ <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">);</span> <span class="comment">// (0 <= alpha <= 1), 0.05 equivalent to 95% confidence.</span>
</pre>
<p>
@@ -362,9 +361,9 @@
Discrete Distributions. Computational statistics and data analysis, 2005,
vol. 48, no3, 605-621</a>.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.estimating_number_of_trials_to_ensure_at_least_a_certain_number_of_failures"></a><h6>
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.estimating_number_of_trials_to_ensure_at_least_a_certain_number_of_failures-heading"></a>
- <a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.estimating_number_of_trials_to_ensure_at_least_a_certain_number_of_failures">Estimating
+<h6>
+<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.h6"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.geometric_dist.estimating_number_of_trials_to_ensure_at_least_a_certain_number_of_failures"></a></span><a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.estimating_number_of_trials_to_ensure_at_least_a_certain_number_of_failures">Estimating
Number of Trials to Ensure at Least a Certain Number of Failures</a>
</h6>
<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_minimum_number_of_trials</span><span class="special">(</span>
@@ -414,9 +413,9 @@
the number of trials (failures) that will lead to an <span class="emphasis"><em>alpha</em></span>
probability of observing <span class="emphasis"><em>k</em></span> failures or fewer.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.estimating_number_of_trials_to_ensure_a_maximum_number_of_failures_or_less"></a><h6>
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.estimating_number_of_trials_to_ensure_a_maximum_number_of_failures_or_less-heading"></a>
- <a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.estimating_number_of_trials_to_ensure_a_maximum_number_of_failures_or_less">Estimating
+<h6>
+<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.h7"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.geometric_dist.estimating_number_of_trials_to_ensure_a_maximum_number_of_failures_or_less"></a></span><a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.estimating_number_of_trials_to_ensure_a_maximum_number_of_failures_or_less">Estimating
Number of Trials to Ensure a Maximum Number of Failures or Less</a>
</h6>
<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_maximum_number_of_trials</span><span class="special">(</span>
@@ -462,9 +461,9 @@
the number of trials that will lead to an <span class="emphasis"><em>alpha</em></span>
probability of observing more than k failures.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.non_member_accessors-heading"></a>
- <a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.h8"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.geometric_dist.non_member_accessors"></a></span><a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -516,7 +515,6 @@
success fraction p. For example:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">pdf</span><span class="special">(</span><span class="identifier">geometric</span><span class="special">(</span><span class="identifier">p</span><span class="special">),</span> <span class="identifier">k</span><span class="special">)</span></pre>
<p>
@@ -536,7 +534,6 @@
success fraction p and success on the last trial. For example:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">geometric</span><span class="special">(</span><span class="identifier">p</span><span class="special">),</span> <span class="identifier">k</span><span class="special">)</span></pre>
<p>
@@ -557,7 +554,6 @@
success fraction p and success on the last trial. For example:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">geometric</span><span class="special">(</span><span class="identifier">p</span><span class="special">),</span> <span class="identifier">k</span><span class="special">))</span></pre>
<p>
@@ -578,7 +574,7 @@
<span class="emphasis"><em>P</em></span>. Note that the value returned is a real-number,
and not an integer. Depending on the use case you may want
to take either the floor or ceiling of the real result. For
- example:
+ example:
</p>
<pre class="programlisting"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">geometric</span><span class="special">(</span><span class="identifier">p</span><span class="special">),</span> <span class="identifier">P</span><span class="special">)</span></pre>
<p>
@@ -600,7 +596,7 @@
<span class="emphasis"><em>P</em></span>. Note that the value returned is a real-number,
and not an integer. Depending on the use case you may want
to take either the floor or ceiling of the real result. For
- example:
+ example:
</p>
<pre class="programlisting"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">geometric</span><span class="special">(</span><span class="identifier">p</span><span class="special">),</span> <span class="identifier">P</span><span class="special">))</span></pre>
<p>
@@ -610,9 +606,9 @@
</tbody>
</table></div>
</div>
-<br class="table-break"><a name="math_toolkit.dist.dist_ref.dists.geometric_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.accuracy-heading"></a>
- <a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.accuracy">Accuracy</a>
+<br class="table-break"><h5>
+<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.h9"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.geometric_dist.accuracy"></a></span><a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.accuracy">Accuracy</a>
</h5>
<p>
This distribution is implemented using the pow and exp functions, so
@@ -621,9 +617,9 @@
<span class="emphasis"><em>p</em></span>, for example 0.9999999999, accuracy can fall significantly,
for example to 10 decimal digits (from 16).
</p>
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.implementation-heading"></a>
- <a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.h10"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.geometric_dist.implementation"></a></span><a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.implementation">Implementation</a>
</h5>
<p>
In the following table, <span class="emphasis"><em>p</em></span> is the probability that
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,7 +28,6 @@
Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">hypergeometric</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
@@ -101,9 +100,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/hypergeometric_pdf_2.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.member_functions-heading"></a>
- <a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.member_functions"></a></span><a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">hypergeometric_distribution</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">r</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">N</span><span class="special">);</span>
@@ -130,9 +129,9 @@
Returns the number of objects <span class="emphasis"><em>n</em></span> which are sampled
from the population <span class="emphasis"><em>N</em></span>.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.non_member_accessors-heading"></a>
- <a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.non_member_accessors"></a></span><a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -184,9 +183,9 @@
</p>
</td></tr>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.accuracy-heading"></a>
- <a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.accuracy"></a></span><a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.accuracy">Accuracy</a>
</h5>
<p>
For small N such that <code class="computeroutput"><span class="identifier">N</span> <span class="special"><</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">max_factorial</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">>::</span><span class="identifier">value</span></code>
@@ -210,9 +209,9 @@
digits of precision during the calculation, with the results becoming
meaningless for N >= 10<sup>15</sup>.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.testing"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.testing-heading"></a>
- <a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.testing">Testing</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.testing"></a></span><a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.testing">Testing</a>
</h5>
<p>
There are three sets of tests: our implementation is tested against a
@@ -222,9 +221,9 @@
Finally we test accuracy against some high precision test data using
this implementation and NTL::RR.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.implementation-heading"></a>
- <a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.implementation"></a></span><a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.implementation">Implementation</a>
</h5>
<p>
The PDF can be calculated directly using the formula:
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,14 +28,13 @@
Chi Squared Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">inverse_chi_squared</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
-
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">inverse_chi_squared_distribution</span>
<span class="special">{</span>
@@ -139,7 +138,6 @@
typedef:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">inverse_chi_squared_distribution</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">inverse_chi_squared</span><span class="special">;</span></pre>
<p>
@@ -149,7 +147,6 @@
inverse_chi_squared distribution you can use
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">inverse_chi_squared_distribution</span><span class="special"><></span></pre>
<p>
@@ -197,9 +194,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/inverse_chi_squared_cdf.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.member_functions-heading"></a>
- <a class="link" href="inverse_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.member_functions"></a></span><a class="link" href="inverse_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">inverse_chi_squared_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">df</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span> <span class="comment">// Implicitly scaled 1/df.</span>
@@ -214,19 +211,19 @@
Requires that the degrees of freedom ν parameter is greater than zero,
otherwise calls <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
</p>
-<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">degrees_of_freedom</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">degrees_of_freedom</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
</pre>
<p>
Returns the degrees_of_freedom ν parameter of this distribution.
</p>
-<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
</pre>
<p>
Returns the scale ξ parameter of this distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.non_member_accessors-heading"></a>
- <a class="link" href="inverse_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.non_member_accessors"></a></span><a class="link" href="inverse_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -254,9 +251,9 @@
equal to zero as a special case, returning zero for both pdf and cdf.
</p></td></tr>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.accuracy-heading"></a>
- <a class="link" href="inverse_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.accuracy"></a></span><a class="link" href="inverse_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.accuracy">Accuracy</a>
</h5>
<p>
The inverse gamma distribution is implemented in terms of the incomplete
@@ -270,9 +267,9 @@
to a few epsilon, >14 decimal digits accuracy for 64-bit double. unless
iteration is involved, as for the estimation of degrees of freedom.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.implementation-heading"></a>
- <a class="link" href="inverse_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.implementation"></a></span><a class="link" href="inverse_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.implementation">Implementation</a>
</h5>
<p>
In the following table ν is the degrees of freedom parameter and ξ is the
@@ -451,9 +448,9 @@
</tr>
</tbody>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.references"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.references-heading"></a>
- <a class="link" href="inverse_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.references">References</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.references"></a></span><a class="link" href="inverse_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.references">References</a>
</h5>
<div class="orderedlist"><ol class="orderedlist" type="1">
<li class="listitem">
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,14 +28,13 @@
Gamma Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">inverse_gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
-
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">inverse_gamma_distribution</span>
<span class="special">{</span>
@@ -85,7 +84,6 @@
distribution <span class="bold"><strong>does</strong></span> provide the typedef:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">inverse_gamma_distribution</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">gamma</span><span class="special">;</span></pre>
<p>
@@ -95,7 +93,6 @@
gamma distribution you can use
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">inverse_gamma_distribution</span><span class="special"><></span></pre>
<p>
@@ -129,9 +126,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/inverse_gamma_cdf.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.member_functions-heading"></a>
- <a class="link" href="inverse_gamma_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.member_functions"></a></span><a class="link" href="inverse_gamma_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">inverse_gamma_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">shape</span> <span class="special">=</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
@@ -153,9 +150,9 @@
<p>
Returns the β scale parameter of this inverse gamma distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.non_member_accessors-heading"></a>
- <a class="link" href="inverse_gamma_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.non_member_accessors"></a></span><a class="link" href="inverse_gamma_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -183,9 +180,9 @@
equal to zero as a special case, returning zero for pdf and cdf.
</p></td></tr>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.accuracy-heading"></a>
- <a class="link" href="inverse_gamma_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.accuracy"></a></span><a class="link" href="inverse_gamma_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.accuracy">Accuracy</a>
</h5>
<p>
The inverse gamma distribution is implemented in terms of the incomplete
@@ -197,9 +194,9 @@
But in general, inverse_gamma results are accurate to a few epsilon,
>14 decimal digits accuracy for 64-bit double.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.implementation-heading"></a>
- <a class="link" href="inverse_gamma_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.implementation"></a></span><a class="link" href="inverse_gamma_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.implementation">Implementation</a>
</h5>
<p>
In the following table α is the shape parameter of the distribution, α   is
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,14 +28,13 @@
Gaussian (or Inverse Normal) Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">inverse_gaussian</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
-
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">inverse_gaussian_distribution</span>
<span class="special">{</span>
@@ -100,7 +99,6 @@
inverse_gaussian distribution you can use
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">inverse_gaussian_distribution</span><span class="special"><></span></pre>
<p>
@@ -145,9 +143,9 @@
by Chhikara and Folks on page 105. Another related parameterisation,
the __wald_distrib (where mean μ is unity) is also provided.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.member_functions-heading"></a>
- <a class="link" href="inverse_gaussian_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.member_functions"></a></span><a class="link" href="inverse_gaussian_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">inverse_gaussian_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">df</span> <span class="special">=</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span> <span class="comment">// optionally scaled.</span>
@@ -160,19 +158,19 @@
Requires that both the mean μ parameter and scale λ are greater than zero,
otherwise calls <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
</p>
-<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">mean</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">mean</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
</pre>
<p>
Returns the mean μ parameter of this distribution.
</p>
-<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
</pre>
<p>
Returns the scale λ parameter of this distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.non_member_accessors-heading"></a>
- <a class="link" href="inverse_gaussian_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.non_member_accessors"></a></span><a class="link" href="inverse_gaussian_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -200,9 +198,9 @@
equal to zero as a special case, returning zero for both pdf and cdf.
</p></td></tr>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.accuracy-heading"></a>
- <a class="link" href="inverse_gaussian_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.accuracy"></a></span><a class="link" href="inverse_gaussian_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.accuracy">Accuracy</a>
</h5>
<p>
The inverse_gaussian distribution is implemented in terms of the exponential
@@ -211,9 +209,9 @@
But in general, gamma (and thus inverse gamma) results are often accurate
to a few epsilon, >14 decimal digits accuracy for 64-bit double.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.implementation-heading"></a>
- <a class="link" href="inverse_gaussian_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.implementation"></a></span><a class="link" href="inverse_gaussian_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.implementation">Implementation</a>
</h5>
<p>
In the following table μ is the mean parameter and λ is the scale parameter
@@ -389,9 +387,9 @@
</tr>
</tbody>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.references"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.references-heading"></a>
- <a class="link" href="inverse_gaussian_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.references">References</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.references"></a></span><a class="link" href="inverse_gaussian_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.references">References</a>
</h5>
<div class="orderedlist"><ol class="orderedlist" type="1">
<li class="listitem">
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,7 +28,6 @@
Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">laplace</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
@@ -80,9 +79,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/laplace_pdf.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.member_functions-heading"></a>
- <a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.laplace_dist.member_functions"></a></span><a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">laplace_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">location</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
@@ -112,9 +111,9 @@
<p>
Returns the <span class="emphasis"><em>scale</em></span> parameter of this distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.non_member_accessors-heading"></a>
- <a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.laplace_dist.non_member_accessors"></a></span><a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -132,17 +131,17 @@
<p>
The domain of the random variable is [-∞,+∞].
</p>
-<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.accuracy-heading"></a>
- <a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.laplace_dist.accuracy"></a></span><a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.accuracy">Accuracy</a>
</h5>
<p>
The laplace distribution is implemented in terms of the standard library
log and exp functions and as such should have very small errors.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.implementation-heading"></a>
- <a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.laplace_dist.implementation"></a></span><a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.implementation">Implementation</a>
</h5>
<p>
In the following table μ is the location parameter of the distribution,
@@ -328,9 +327,9 @@
</tr>
</tbody>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.references"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.references-heading"></a>
- <a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.references">References</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.laplace_dist.references"></a></span><a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.references">References</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,14 +28,13 @@
Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">logistic</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
-
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">logistic_distribution</span><span class="special">;</span>
@@ -50,7 +49,7 @@
<span class="comment">// Accessors:</span>
<span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> <span class="comment">// location.</span>
<span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> <span class="comment">// scale.</span>
-
+
<span class="special">};</span>
<span class="keyword">typedef</span> <span class="identifier">logistic_distribution</span><span class="special"><></span> <span class="identifier">logistic</span><span class="special">;</span>
@@ -71,9 +70,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/logistic_pdf.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.member_functions-heading"></a>
- <a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.logistic_dist.member_functions"></a></span><a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">logistic_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">u</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">s</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
@@ -87,7 +86,7 @@
<span class="number">0</span></code>, otherwise a <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>
is raised.
</p>
-<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
</pre>
<p>
Returns the location of this distribution.
@@ -97,9 +96,9 @@
<p>
Returns the scale of this distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.non_member_accessors-heading"></a>
- <a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.logistic_dist.non_member_accessors"></a></span><a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -127,9 +126,9 @@
complement quantile function returns the result of -<a class="link" href="../../../main_overview/error_handling.html#overflow_error">overflow_error</a>
and +<a class="link" href="../../../main_overview/error_handling.html#overflow_error">overflow_error</a> respectively.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.accuracy-heading"></a>
- <a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.logistic_dist.accuracy"></a></span><a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.accuracy">Accuracy</a>
</h5>
<p>
The logistic distribution is implemented in terms of the <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span></code> and the <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">log</span></code>
@@ -139,9 +138,9 @@
cancellation errors can occur: in such cases, only a low <span class="emphasis"><em>absolute
error</em></span> can be guarenteed.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.implementation-heading"></a>
- <a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.logistic_dist.implementation"></a></span><a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.implementation">Implementation</a>
</h5>
<div class="informaltable"><table class="table">
<colgroup>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,14 +28,13 @@
Normal Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">lognormal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
-
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">lognormal_distribution</span><span class="special">;</span>
@@ -87,9 +86,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/lognormal_pdf2.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.member_functions-heading"></a>
- <a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.member_functions"></a></span><a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">lognormal_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">location</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
@@ -120,9 +119,9 @@
<p>
Returns the <span class="emphasis"><em>scale</em></span> parameter of this distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.non_member_accessors-heading"></a>
- <a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.non_member_accessors"></a></span><a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -140,18 +139,18 @@
<p>
The domain of the random variable is [0,+∞].
</p>
-<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.accuracy-heading"></a>
- <a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.accuracy"></a></span><a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.accuracy">Accuracy</a>
</h5>
<p>
The lognormal distribution is implemented in terms of the standard library
log and exp functions, plus the <a class="link" href="../../../special/sf_erf/error_function.html" title="Error Functions">error
function</a>, and as such should have very low error rates.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.implementation-heading"></a>
- <a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.implementation"></a></span><a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.implementation">Implementation</a>
</h5>
<p>
In the following table <span class="emphasis"><em>m</em></span> is the location parameter
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,14 +28,13 @@
Beta Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">non_central_beta</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">non_central_beta_distribution</span><span class="special">;</span>
@@ -95,9 +94,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/nc_beta_pdf.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.member_functions-heading"></a>
- <a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.member_functions"></a></span><a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">non_central_beta_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">lambda</span><span class="special">);</span>
@@ -127,9 +126,9 @@
Returns the parameter <span class="emphasis"><em>lambda</em></span> from which this object
was constructed.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.non_member_accessors-heading"></a>
- <a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.non_member_accessors"></a></span><a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -155,9 +154,9 @@
<p>
The domain of the random variable is [0, 1].
</p>
-<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.accuracy-heading"></a>
- <a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.accuracy"></a></span><a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.accuracy">Accuracy</a>
</h5>
<p>
The following table shows the peak errors (in units of epsilon)
@@ -298,9 +297,9 @@
Error rates for the PDF, the complement of the CDF and for the quantile
functions are broadly similar.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.tests"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.tests-heading"></a>
- <a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.tests">Tests</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.tests"></a></span><a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.tests">Tests</a>
</h5>
<p>
There are two sets of test data used to verify this implementation: firstly
@@ -310,9 +309,9 @@
be accurate to at least 50 decimal digits - and is the used for our accuracy
tests.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.implementation-heading"></a>
- <a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.implementation"></a></span><a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.implementation">Implementation</a>
</h5>
<p>
The CDF and its complement are evaluated as follows:
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,14 +28,13 @@
Chi-Squared Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">non_central_chi_squared</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">non_central_chi_squared_distribution</span><span class="special">;</span>
@@ -61,7 +60,7 @@
<span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_degrees_of_freedom</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">lambda</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">A</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">B</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">C</span><span class="special">></span>
<span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_degrees_of_freedom</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">complemented3_type</span><span class="special"><</span><span class="identifier">A</span><span class="special">,</span><span class="identifier">B</span><span class="special">,</span><span class="identifier">C</span><span class="special">>&</span> <span class="identifier">c</span><span class="special">);</span>
-
+
<span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_non_centrality</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">A</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">B</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">C</span><span class="special">></span>
<span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_non_centrality</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">complemented3_type</span><span class="special"><</span><span class="identifier">A</span><span class="special">,</span><span class="identifier">B</span><span class="special">,</span><span class="identifier">C</span><span class="special">>&</span> <span class="identifier">c</span><span class="special">);</span>
@@ -109,9 +108,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/nccs_pdf.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.member_functions-heading"></a>
- <a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.member_functions"></a></span><a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">non_central_chi_squared_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">lambda</span><span class="special">);</span>
@@ -182,9 +181,9 @@
<span class="identifier">x</span><span class="special">))</span>
<span class="special">==</span> <span class="identifier">q</span></code>.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.non_member_accessors-heading"></a>
- <a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.non_member_accessors"></a></span><a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -202,17 +201,17 @@
<p>
The domain of the random variable is [0, +∞].
</p>
-<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.examples"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.examples-heading"></a>
- <a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.examples">Examples</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.examples"></a></span><a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.examples">Examples</a>
</h5>
<p>
There is a <a class="link" href="../../stat_tut/weg/nccs_eg.html" title="Non Central Chi Squared Example">worked
example</a> for the noncentral chi-squared distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.accuracy-heading"></a>
- <a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.accuracy"></a></span><a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.accuracy">Accuracy</a>
</h5>
<p>
The following table shows the peak errors (in units of epsilon)
@@ -358,9 +357,9 @@
numerically by finding the maxima of the PDF: in principal this can not
produce an accuracy greater than the square root of the machine epsilon.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.tests"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.tests-heading"></a>
- <a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.tests">Tests</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.tests"></a></span><a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.tests">Tests</a>
</h5>
<p>
There are two sets of test data used to verify this implementation: firstly
@@ -372,9 +371,9 @@
implementation and using interval arithmetic - this data should be accurate
to at least 50 decimal digits - and is the used for our accuracy tests.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.implementation-heading"></a>
- <a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.h5"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.implementation"></a></span><a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.implementation">Implementation</a>
</h5>
<p>
The CDF and its complement are evaluated as follows:
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,14 +28,13 @@
F Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">non_central_f</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">non_central_f_distribution</span><span class="special">;</span>
@@ -94,9 +93,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/nc_f_pdf.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.member_functions-heading"></a>
- <a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.member_functions"></a></span><a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">non_central_f_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">v1</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">v2</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">lambda</span><span class="special">);</span>
@@ -126,9 +125,9 @@
Returns the non-centrality parameter <span class="emphasis"><em>lambda</em></span> from
which this object was constructed.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.non_member_accessors-heading"></a>
- <a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.non_member_accessors"></a></span><a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -146,26 +145,26 @@
<p>
The domain of the random variable is [0, +∞].
</p>
-<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.accuracy-heading"></a>
- <a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.accuracy"></a></span><a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.accuracy">Accuracy</a>
</h5>
<p>
This distribution is implemented in terms of the <a class="link" href="nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral
Beta Distribution</a>: refer to that distribution for accuracy data.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.tests"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.tests-heading"></a>
- <a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.tests">Tests</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.tests"></a></span><a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.tests">Tests</a>
</h5>
<p>
Since this distribution is implemented by adapting another distribution,
the tests consist of basic sanity checks computed by the <a href="http://www.r-project.org/" target="_top">R-2.5.1
Math library statistical package</a> and its pbeta and dbeta functions.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.implementation-heading"></a>
- <a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.implementation"></a></span><a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.implementation">Implementation</a>
</h5>
<p>
In the following table <span class="emphasis"><em>v1</em></span> and <span class="emphasis"><em>v2</em></span>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,14 +28,13 @@
T Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">non_central_t</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">non_central_t_distribution</span><span class="special">;</span>
@@ -84,9 +83,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/nc_t_pdf.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.member_functions-heading"></a>
- <a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.member_functions"></a></span><a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">non_central_t_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">lambda</span><span class="special">);</span>
@@ -110,9 +109,9 @@
Returns the non-centrality parameter <span class="emphasis"><em>delta</em></span> from
which this object was constructed.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.non_member_accessors-heading"></a>
- <a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.non_member_accessors"></a></span><a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -130,9 +129,9 @@
<p>
The domain of the random variable is [-∞, +∞].
</p>
-<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.accuracy-heading"></a>
- <a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.accuracy"></a></span><a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.accuracy">Accuracy</a>
</h5>
<p>
The following table shows the peak errors (in units of epsilon)
@@ -254,9 +253,9 @@
and can not in principal be more accurate than the square root of machine
epsilon.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.tests"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.tests-heading"></a>
- <a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.tests">Tests</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.tests"></a></span><a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.tests">Tests</a>
</h5>
<p>
There are two sets of tests of this distribution: basic sanity checks
@@ -269,9 +268,9 @@
interval arithmetic: this test data is believed to be accurate to at
least 50 decimal places.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.implementation-heading"></a>
- <a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.implementation"></a></span><a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.implementation">Implementation</a>
</h5>
<p>
The CDF is computed using a modification of the method described in "Computing
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,14 +28,13 @@
Binomial Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">negative_binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">negative_binomial_distribution</span><span class="special">;</span>
@@ -49,21 +48,21 @@
<span class="keyword">typedef</span> <span class="identifier">Policy</span> <span class="identifier">policy_type</span><span class="special">;</span>
<span class="comment">// Constructor from successes and success_fraction:</span>
<span class="identifier">negative_binomial_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">r</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
-
+
<span class="comment">// Parameter accessors:</span>
<span class="identifier">RealType</span> <span class="identifier">success_fraction</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
-
+
<span class="comment">// Bounds on success fraction:</span>
<span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_lower_bound_on_p</span><span class="special">(</span>
- <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span>
+ <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">probability</span><span class="special">);</span> <span class="comment">// alpha</span>
<span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_upper_bound_on_p</span><span class="special">(</span>
- <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span>
+ <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">probability</span><span class="special">);</span> <span class="comment">// alpha</span>
-
+
<span class="comment">// Estimate min/max number of trials:</span>
<span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_minimum_number_of_trials</span><span class="special">(</span>
<span class="identifier">RealType</span> <span class="identifier">k</span><span class="special">,</span> <span class="comment">// Number of failures.</span>
@@ -122,9 +121,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/negative_binomial_pdf_2.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.related_distributions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.related_distributions-heading"></a>
- <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.related_distributions">Related
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.related_distributions"></a></span><a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.related_distributions">Related
Distributions</a>
</h5>
<p>
@@ -194,14 +193,14 @@
</p>
</td></tr>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.member_functions-heading"></a>
- <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.member_functions"></a></span><a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.member_functions">Member
Functions</a>
</h5>
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.construct"></a><h6>
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.construct-heading"></a>
- <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.construct">Construct</a>
+<h6>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.construct"></a></span><a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.construct">Construct</a>
</h6>
<pre class="programlisting"><span class="identifier">negative_binomial_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">r</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
</pre>
@@ -215,9 +214,9 @@
<span class="special"><=</span> <span class="identifier">p</span>
<span class="special"><=</span> <span class="number">1</span></code>.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accessors"></a><h6>
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accessors-heading"></a>
- <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accessors">Accessors</a>
+<h6>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accessors"></a></span><a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accessors">Accessors</a>
</h6>
<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">success_fraction</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> <span class="comment">// successes / trials (0 <= p <= 1)</span>
</pre>
@@ -236,13 +235,13 @@
see <a class="link" href="binomial_dist.html" title="Binomial Distribution">Binomial
Distribution</a> for more discussion.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.lower_bound_on_parameter_p"></a><h6>
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.lower_bound_on_parameter_p-heading"></a>
- <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.lower_bound_on_parameter_p">Lower
+<h6>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.lower_bound_on_parameter_p"></a></span><a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.lower_bound_on_parameter_p">Lower
Bound on Parameter p</a>
</h6>
<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_lower_bound_on_p</span><span class="special">(</span>
- <span class="identifier">RealType</span> <span class="identifier">failures</span><span class="special">,</span>
+ <span class="identifier">RealType</span> <span class="identifier">failures</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">probability</span><span class="special">)</span> <span class="comment">// (0 <= alpha <= 1), 0.05 equivalent to 95% confidence.</span>
</pre>
@@ -297,13 +296,13 @@
Discrete Distributions. Computational statistics and data analysis, 2005,
vol. 48, no3, 605-621</a>.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.upper_bound_on_parameter_p"></a><h6>
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.upper_bound_on_parameter_p-heading"></a>
- <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.upper_bound_on_parameter_p">Upper
+<h6>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.h5"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.upper_bound_on_parameter_p"></a></span><a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.upper_bound_on_parameter_p">Upper
Bound on Parameter p</a>
</h6>
<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_upper_bound_on_p</span><span class="special">(</span>
- <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span>
+ <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">,</span>
<span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">);</span> <span class="comment">// (0 <= alpha <= 1), 0.05 equivalent to 95% confidence.</span>
</pre>
@@ -357,9 +356,9 @@
Discrete Distributions. Computational statistics and data analysis, 2005,
vol. 48, no3, 605-621</a>.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_at_least_a_certain_number_of_failures"></a><h6>
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_at_least_a_certain_number_of_failures-heading"></a>
- <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_at_least_a_certain_number_of_failures">Estimating
+<h6>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.h6"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_at_least_a_certain_number_of_failures"></a></span><a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_at_least_a_certain_number_of_failures">Estimating
Number of Trials to Ensure at Least a Certain Number of Failures</a>
</h6>
<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_minimum_number_of_trials</span><span class="special">(</span>
@@ -408,9 +407,9 @@
finds the number of trials (success+failures) that will lead to an <span class="emphasis"><em>alpha</em></span>
probability of observing k failures or fewer.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_a_maximum_number_of_failures_or_less"></a><h6>
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_a_maximum_number_of_failures_or_less-heading"></a>
- <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_a_maximum_number_of_failures_or_less">Estimating
+<h6>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.h7"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_a_maximum_number_of_failures_or_less"></a></span><a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_a_maximum_number_of_failures_or_less">Estimating
Number of Trials to Ensure a Maximum Number of Failures or Less</a>
</h6>
<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_maximum_number_of_trials</span><span class="special">(</span>
@@ -456,9 +455,9 @@
finds the number of trials (success+failures) that will lead to an <span class="emphasis"><em>alpha</em></span>
probability of observing more than k failures.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.non_member_accessors-heading"></a>
- <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.h8"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.non_member_accessors"></a></span><a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -510,7 +509,6 @@
p. For example:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">pdf</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">p</span><span class="special">),</span> <span class="identifier">k</span><span class="special">)</span></pre>
<p>
@@ -530,7 +528,6 @@
and success on the last trial. For example:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">p</span><span class="special">),</span> <span class="identifier">k</span><span class="special">)</span></pre>
<p>
@@ -551,7 +548,6 @@
p and success on the last trial. For example:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">p</span><span class="special">),</span> <span class="identifier">k</span><span class="special">))</span></pre>
<p>
@@ -574,7 +570,6 @@
example:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">p</span><span class="special">),</span> <span class="identifier">P</span><span class="special">)</span></pre>
<p>
@@ -595,7 +590,7 @@
p, at probability P. Note that the value returned is a real-number,
and not an integer. Depending on the use case you may want
to take either the floor or ceiling of the real result. For
- example:
+ example:
</p>
<pre class="programlisting"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">p</span><span class="special">),</span> <span class="identifier">P</span><span class="special">))</span></pre>
<p>
@@ -605,9 +600,9 @@
</tbody>
</table></div>
</div>
-<br class="table-break"><a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accuracy-heading"></a>
- <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accuracy">Accuracy</a>
+<br class="table-break"><h5>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.h9"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accuracy"></a></span><a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accuracy">Accuracy</a>
</h5>
<p>
This distribution is implemented using the incomplete beta functions
@@ -615,9 +610,9 @@
and <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>:
please refer to these functions for information on accuracy.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.implementation-heading"></a>
- <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.h10"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.implementation"></a></span><a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.implementation">Implementation</a>
</h5>
<p>
In the following table, <span class="emphasis"><em>p</em></span> is the probability that
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,14 +28,13 @@
(Gaussian) Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
-
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">normal_distribution</span><span class="special">;</span>
@@ -78,9 +77,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/normal_pdf.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.normal_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.normal_dist.member_functions-heading"></a>
- <a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.normal_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.normal_dist.member_functions"></a></span><a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">normal_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">mean</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">sd</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
@@ -94,7 +93,7 @@
is called.
</p>
<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">mean</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
-<span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+<span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
</pre>
<p>
both return the <span class="emphasis"><em>mean</em></span> of this distribution.
@@ -108,9 +107,9 @@
distributions, allowing the functions find_location and find_scale to
be used generically).
</p>
-<a name="math_toolkit.dist.dist_ref.dists.normal_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.normal_dist.non_member_accessors-heading"></a>
- <a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.normal_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.normal_dist.non_member_accessors"></a></span><a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -130,17 +129,17 @@
the pdf of +∞ and -∞ = 0 is also supported, and cdf at -∞ = 0, cdf at +∞ = 1,
and complement cdf -∞ = 1 and +∞ = 0, if RealType permits.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.normal_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.normal_dist.accuracy-heading"></a>
- <a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.normal_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.normal_dist.accuracy"></a></span><a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.accuracy">Accuracy</a>
</h5>
<p>
The normal distribution is implemented in terms of the <a class="link" href="../../../special/sf_erf/error_function.html" title="Error Functions">error
function</a>, and as such should have very low error rates.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.normal_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.normal_dist.implementation-heading"></a>
- <a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.normal_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.normal_dist.implementation"></a></span><a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.implementation">Implementation</a>
</h5>
<p>
In the following table <span class="emphasis"><em>m</em></span> is the mean of the distribution,
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -27,7 +27,6 @@
<a name="math_toolkit.dist.dist_ref.dists.pareto"></a><a class="link" href="pareto.html" title="Pareto Distribution">Pareto Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">pareto</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
@@ -85,14 +84,14 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/pareto_pdf2.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.pareto.related_distributions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.pareto.related_distributions-heading"></a>
- <a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.related_distributions">Related
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.pareto.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.pareto.related_distributions"></a></span><a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.related_distributions">Related
distributions</a>
</h5>
-<a name="math_toolkit.dist.dist_ref.dists.pareto.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.pareto.member_functions-heading"></a>
- <a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.pareto.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.pareto.member_functions"></a></span><a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">pareto_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">shape</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
@@ -116,9 +115,9 @@
<p>
Returns the <span class="emphasis"><em>shape</em></span> parameter of this distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.pareto.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.pareto.non_member_accessors-heading"></a>
- <a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.pareto.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.pareto.non_member_accessors"></a></span><a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -136,9 +135,9 @@
<p>
The supported domain of the random variable is [scale, ∞].
</p>
-<a name="math_toolkit.dist.dist_ref.dists.pareto.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.pareto.accuracy-heading"></a>
- <a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.pareto.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.pareto.accuracy"></a></span><a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.accuracy">Accuracy</a>
</h5>
<p>
The Pareto distribution is implemented in terms of the standard library
@@ -149,9 +148,9 @@
If probability is near to unity (or the complement of a probability near
zero) see also <a class="link" href="../../stat_tut/overview/complements.html#why_complements">why complements?</a>.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.pareto.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.pareto.implementation-heading"></a>
- <a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.pareto.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.pareto.implementation"></a></span><a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.implementation">Implementation</a>
</h5>
<p>
In the following table α   is the shape parameter of the distribution, and
@@ -317,9 +316,9 @@
</tr>
</tbody>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.pareto.references"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.pareto.references-heading"></a>
- <a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.references">References</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.pareto.h5"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.pareto.references"></a></span><a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.references">References</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,14 +28,13 @@
Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">poisson</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">poisson_distribution</span><span class="special">;</span>
@@ -43,15 +42,15 @@
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">></span>
<span class="keyword">class</span> <span class="identifier">poisson_distribution</span>
-<span class="special">{</span>
+<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
<span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">Policy</span> <span class="identifier">policy_type</span><span class="special">;</span>
-
+
<span class="identifier">poisson_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">mean</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span> <span class="comment">// Constructor.</span>
<span class="identifier">RealType</span> <span class="identifier">mean</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> <span class="comment">// Accessor.</span>
<span class="special">}</span>
-
+
<span class="special">}}</span> <span class="comment">// namespaces boost::math</span>
</pre>
<p>
@@ -115,9 +114,9 @@
</p>
</td></tr>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.member_functions-heading"></a>
- <a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.poisson_dist.member_functions"></a></span><a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">poisson_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">mean</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
@@ -130,9 +129,9 @@
<p>
Returns the <span class="emphasis"><em>mean</em></span> of this distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.non_member_accessors-heading"></a>
- <a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.poisson_dist.non_member_accessors"></a></span><a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -150,9 +149,9 @@
<p>
The domain of the random variable is [0, ∞].
</p>
-<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.accuracy-heading"></a>
- <a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.poisson_dist.accuracy"></a></span><a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.accuracy">Accuracy</a>
</h5>
<p>
The Poisson distribution is implemented in terms of the incomplete gamma
@@ -164,9 +163,9 @@
accurate: this is because the inverse gamma functions are implemented
using an iterative method with a lower tolerance to avoid excessive computation.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.implementation-heading"></a>
- <a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.poisson_dist.implementation"></a></span><a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.implementation">Implementation</a>
</h5>
<p>
In the following table λ   is the mean of the distribution, <span class="emphasis"><em>k</em></span>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,14 +28,13 @@
Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">rayleigh</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
-
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">rayleigh_distribution</span><span class="special">;</span>
@@ -85,9 +84,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/rayleigh_cdf.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.rayleigh.related_distributions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.rayleigh.related_distributions-heading"></a>
- <a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.related_distributions">Related
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.rayleigh.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.rayleigh.related_distributions"></a></span><a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.related_distributions">Related
distributions</a>
</h5>
<p>
@@ -101,9 +100,9 @@
distributions are generalizations of the <a href="http://en.wikipedia.org/wiki/Rayleigh_distribution" target="_top">Rayleigh
distribution</a>.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.rayleigh.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.rayleigh.member_functions-heading"></a>
- <a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.rayleigh.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.rayleigh.member_functions"></a></span><a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">rayleigh_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">sigma</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
@@ -120,9 +119,9 @@
<p>
Returns the <span class="emphasis"><em>sigma</em></span> parameter of this distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.rayleigh.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.rayleigh.non_member_accessors-heading"></a>
- <a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.rayleigh.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.rayleigh.non_member_accessors"></a></span><a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -140,9 +139,9 @@
<p>
The domain of the random variable is [0, max_value].
</p>
-<a name="math_toolkit.dist.dist_ref.dists.rayleigh.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.rayleigh.accuracy-heading"></a>
- <a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.rayleigh.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.rayleigh.accuracy"></a></span><a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.accuracy">Accuracy</a>
</h5>
<p>
The Rayleigh distribution is implemented in terms of the standard library
@@ -150,9 +149,9 @@
error rates. Some constants such as skewness and kurtosis were calculated
using NTL RR type with 150-bit accuracy, about 50 decimal digits.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.rayleigh.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.rayleigh.implementation-heading"></a>
- <a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.rayleigh.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.rayleigh.implementation"></a></span><a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.implementation">Implementation</a>
</h5>
<p>
In the following table σ   is the sigma parameter of the distribution, <span class="emphasis"><em>x</em></span>
@@ -319,9 +318,9 @@
</tr>
</tbody>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.rayleigh.references"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.rayleigh.references-heading"></a>
- <a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.references">References</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.rayleigh.h5"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.rayleigh.references"></a></span><a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.references">References</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,14 +28,13 @@
t Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">students_t</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
-
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">students_t_distribution</span><span class="special">;</span>
@@ -46,13 +45,13 @@
<span class="special">{</span>
<span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">Policy</span> <span class="identifier">policy_type</span><span class="special">;</span>
-
+
<span class="comment">// Construct:</span>
<span class="identifier">students_t_distribution</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&</span> <span class="identifier">v</span><span class="special">);</span>
-
+
<span class="comment">// Accessor:</span>
<span class="identifier">RealType</span> <span class="identifier">degrees_of_freedom</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
-
+
<span class="comment">// degrees of freedom estimation:</span>
<span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_degrees_of_freedom</span><span class="special">(</span>
<span class="identifier">RealType</span> <span class="identifier">difference_from_mean</span><span class="special">,</span>
@@ -96,9 +95,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/students_t_pdf.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.member_functions-heading"></a>
- <a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.students_t_dist.member_functions"></a></span><a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">students_t_distribution</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&</span> <span class="identifier">v</span><span class="special">);</span>
@@ -173,9 +172,9 @@
For more information on this function see the <a href="http://www.itl.nist.gov/div898/handbook/prc/section2/prc222.htm" target="_top">NIST
Engineering Statistics Handbook</a>.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.non_member_accessors-heading"></a>
- <a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.students_t_dist.non_member_accessors"></a></span><a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -193,26 +192,26 @@
<p>
The domain of the random variable is [-∞, +∞].
</p>
-<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.examples"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.examples-heading"></a>
- <a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.examples">Examples</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.students_t_dist.examples"></a></span><a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.examples">Examples</a>
</h5>
<p>
Various <a class="link" href="../../stat_tut/weg/st_eg.html" title="Student's t Distribution Examples">worked examples</a>
are available illustrating the use of the Student's t distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.accuracy-heading"></a>
- <a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.students_t_dist.accuracy"></a></span><a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.accuracy">Accuracy</a>
</h5>
<p>
The normal distribution is implemented in terms of the <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">incomplete
beta function</a> and <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">its
inverses</a>, refer to accuracy data on those functions for more information.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.implementation-heading"></a>
- <a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.students_t_dist.implementation"></a></span><a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.implementation">Implementation</a>
</h5>
<p>
In the following table <span class="emphasis"><em>v</em></span> is the degrees of freedom
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,16 +28,15 @@
Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">triangular</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
- <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+ <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">triangular_distribution</span><span class="special">;</span>
-
+
<span class="keyword">typedef</span> <span class="identifier">triangular_distribution</span><span class="special"><></span> <span class="identifier">triangular</span><span class="special">;</span>
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">></span>
@@ -127,9 +126,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/triangular_cdf.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.member_functions-heading"></a>
- <a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.triangular_dist.member_functions"></a></span><a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">triangular_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">lower</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">mode</span> <span class="special">=</span> <span class="number">0</span> <span class="identifier">RealType</span> <span class="identifier">upper</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
@@ -162,9 +161,9 @@
Returns the <span class="emphasis"><em>upper</em></span> parameter of this distribution
(default+1).
</p>
-<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.non_member_accessors-heading"></a>
- <a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.triangular_dist.non_member_accessors"></a></span><a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -183,18 +182,18 @@
The domain of the random variable is \lowerto \upper, and the supported
range is lower <= x <= upper.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.accuracy-heading"></a>
- <a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.triangular_dist.accuracy"></a></span><a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.accuracy">Accuracy</a>
</h5>
<p>
The triangular distribution is implemented with simple arithmetic operators
and so should have errors within an epsilon or two, except quantiles
with arguments nearing the extremes of zero and unity.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.implementation-heading"></a>
- <a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.triangular_dist.implementation"></a></span><a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.implementation">Implementation</a>
</h5>
<p>
In the following table, a is the <span class="emphasis"><em>lower</em></span> parameter
@@ -377,9 +376,9 @@
Some 'known good' test values were obtained from <a href="http://espse.ed.psu.edu/edpsych/faculty/rhale/hale/507Mat/statlets/free/pdist.htm" target="_top">Statlet:
Calculate and plot probability distributions</a>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.references"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.references-heading"></a>
- <a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.references">References</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.triangular_dist.references"></a></span><a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.references">References</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/uniform_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/uniform_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/uniform_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,16 +28,15 @@
Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">uniform</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
- <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+ <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">uniform_distribution</span><span class="special">;</span>
-
+
<span class="keyword">typedef</span> <span class="identifier">uniform_distribution</span><span class="special"><></span> <span class="identifier">uniform</span><span class="special">;</span>
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">></span>
@@ -116,9 +115,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/uniform_cdf.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.member_functions-heading"></a>
- <a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.uniform_dist.member_functions"></a></span><a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">uniform_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">lower</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">upper</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
@@ -143,9 +142,9 @@
<p>
Returns the <span class="emphasis"><em>upper</em></span> parameter of this distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.non_member_accessors-heading"></a>
- <a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.uniform_dist.non_member_accessors"></a></span><a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -164,17 +163,17 @@
The domain of the random variable is any finite value, but the supported
range is only <span class="emphasis"><em>lower</em></span> <= x <= <span class="emphasis"><em>upper</em></span>.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.accuracy-heading"></a>
- <a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.uniform_dist.accuracy"></a></span><a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.accuracy">Accuracy</a>
</h5>
<p>
The uniform distribution is implemented with simple arithmetic operators
and so should have errors within an epsilon or two.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.implementation-heading"></a>
- <a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.uniform_dist.implementation"></a></span><a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.implementation">Implementation</a>
</h5>
<p>
In the following table a is the <span class="emphasis"><em>lower</em></span> parameter
@@ -336,9 +335,9 @@
</tr>
</tbody>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.references"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.references-heading"></a>
- <a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.references">References</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.uniform_dist.references"></a></span><a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.references">References</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/weibull_dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/weibull_dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/weibull_dist.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -28,14 +28,13 @@
Distribution</a>
</h5></div></div></div>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">weibull</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<p>
</p>
-<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
-
-<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">weibull_distribution</span><span class="special">;</span>
@@ -99,9 +98,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/weibull_pdf2.png" align="middle"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.related_distributions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.related_distributions-heading"></a>
- <a class="link" href="weibull_dist.html#math_toolkit.dist.dist_ref.dists.weibull_dist.related_distributions">Related
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.weibull_dist.related_distributions"></a></span><a class="link" href="weibull_dist.html#math_toolkit.dist.dist_ref.dists.weibull_dist.related_distributions">Related
distributions</a>
</h5>
<p>
@@ -113,9 +112,9 @@
distributions, of which the Weibull is but one, is discussed by <a href="http://www.worldscibooks.com/mathematics/p191.html" target="_top">Extreme Value
Distributions, Theory and Applications Samuel Kotz & Saralees Nadarajah</a>.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.member_functions"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.member_functions-heading"></a>
- <a class="link" href="weibull_dist.html#math_toolkit.dist.dist_ref.dists.weibull_dist.member_functions">Member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.weibull_dist.member_functions"></a></span><a class="link" href="weibull_dist.html#math_toolkit.dist.dist_ref.dists.weibull_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">weibull_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">shape</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
@@ -139,9 +138,9 @@
<p>
Returns the <span class="emphasis"><em>scale</em></span> parameter of this distribution.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.non_member_accessors"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.non_member_accessors-heading"></a>
- <a class="link" href="weibull_dist.html#math_toolkit.dist.dist_ref.dists.weibull_dist.non_member_accessors">Non-member
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.weibull_dist.non_member_accessors"></a></span><a class="link" href="weibull_dist.html#math_toolkit.dist.dist_ref.dists.weibull_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
@@ -159,9 +158,9 @@
<p>
The domain of the random variable is [0, ∞].
</p>
-<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.accuracy"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.accuracy-heading"></a>
- <a class="link" href="weibull_dist.html#math_toolkit.dist.dist_ref.dists.weibull_dist.accuracy">Accuracy</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.weibull_dist.accuracy"></a></span><a class="link" href="weibull_dist.html#math_toolkit.dist.dist_ref.dists.weibull_dist.accuracy">Accuracy</a>
</h5>
<p>
The Weibull distribution is implemented in terms of the standard library
@@ -169,9 +168,9 @@
and <a class="link" href="../../../special/powers/log1p.html" title="log1p">log1p</a> and
as such should have very low error rates.
</p>
-<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.implementation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.implementation-heading"></a>
- <a class="link" href="weibull_dist.html#math_toolkit.dist.dist_ref.dists.weibull_dist.implementation">Implementation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.weibull_dist.implementation"></a></span><a class="link" href="weibull_dist.html#math_toolkit.dist.dist_ref.dists.weibull_dist.implementation">Implementation</a>
</h5>
<p>
In the following table α   is the shape parameter of the distribution, β   is
@@ -336,9 +335,9 @@
</tr>
</tbody>
</table></div>
-<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.references"></a><h5>
-<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.references-heading"></a>
- <a class="link" href="weibull_dist.html#math_toolkit.dist.dist_ref.dists.weibull_dist.references">References</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.h5"></a>
+ <span><a name="math_toolkit.dist.dist_ref.dists.weibull_dist.references"></a></span><a class="link" href="weibull_dist.html#math_toolkit.dist.dist_ref.dists.weibull_dist.references">References</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/nmp.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/nmp.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/nmp.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -36,9 +36,9 @@
<a class="link" href="nmp.html#function_index">function index</a> to go straight to
the function you want if you already know its name.
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__function_index___function_index"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__function_index___function_index-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__function_index___function_index"><a name="function_index"></a>Function Index</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h0"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__function_index___function_index"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__function_index___function_index"><a name="function_index"></a>Function Index</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
@@ -93,9 +93,9 @@
<a class="link" href="nmp.html#math.dist.variance">variance</a>.
</li>
</ul></div>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__concept_index___conceptual_index"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__concept_index___conceptual_index-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__concept_index___conceptual_index"><a name="concept_index"></a>Conceptual Index</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h1"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__concept_index___conceptual_index"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__concept_index___conceptual_index"><a name="concept_index"></a>Conceptual Index</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
@@ -179,9 +179,9 @@
<a class="link" href="nmp.html#math.dist.variance">variance</a>.
</li>
</ul></div>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_cdf___cumulative_distribution_function"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_cdf___cumulative_distribution_function-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_cdf___cumulative_distribution_function"><a name="math.dist.cdf"></a>Cumulative Distribution Function</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h2"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_cdf___cumulative_distribution_function"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_cdf___cumulative_distribution_function"><a name="math.dist.cdf"></a>Cumulative Distribution Function</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span>
<span class="identifier">RealType</span> <span class="identifier">cdf</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special"><</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">>&</span> <span class="identifier">dist</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&</span> <span class="identifier">x</span><span class="special">);</span>
@@ -202,9 +202,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../graphs/cdf.png" alt="cdf"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_ccdf___complement_of_the_cumulative_distribution_function"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_ccdf___complement_of_the_cumulative_distribution_function-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_ccdf___complement_of_the_cumulative_distribution_function"><a name="math.dist.ccdf"></a>Complement of the Cumulative Distribution Function</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h3"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_ccdf___complement_of_the_cumulative_distribution_function"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_ccdf___complement_of_the_cumulative_distribution_function"><a name="math.dist.ccdf"></a>Complement of the Cumulative Distribution Function</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Distribution</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">></span>
<span class="identifier">RealType</span> <span class="identifier">cdf</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Unspecified-Complement-Type</em></span><span class="special"><</span><span class="identifier">Distribution</span><span class="special">,</span> <span class="identifier">RealType</span><span class="special">>&</span> <span class="identifier">comp</span><span class="special">);</span>
@@ -242,9 +242,9 @@
See <a class="link" href="../stat_tut/overview/complements.html#why_complements">why complements?</a> for why the
complement is useful and when it should be used.
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_hazard___hazard_function"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_hazard___hazard_function-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_hazard___hazard_function"><a name="math.dist.hazard"></a>Hazard Function</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h4"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_hazard___hazard_function"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_hazard___hazard_function"><a name="math.dist.hazard"></a>Hazard Function</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span>
<span class="identifier">RealType</span> <span class="identifier">hazard</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special"><</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">>&</span> <span class="identifier">dist</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&</span> <span class="identifier">x</span><span class="special">);</span>
@@ -270,9 +270,9 @@
rather than the hazard function.
</p></td></tr>
</table></div>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_chf___cumulative_hazard_function"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_chf___cumulative_hazard_function-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_chf___cumulative_hazard_function"><a name="math.dist.chf"></a>Cumulative Hazard Function</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h5"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_chf___cumulative_hazard_function"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_chf___cumulative_hazard_function"><a name="math.dist.chf"></a>Cumulative Hazard Function</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span>
<span class="identifier">RealType</span> <span class="identifier">chf</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special"><</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">>&</span> <span class="identifier">dist</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&</span> <span class="identifier">x</span><span class="special">);</span>
@@ -297,9 +297,9 @@
Some authors refer to this as simply the "Hazard Function".
</p></td></tr>
</table></div>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_mean___mean"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_mean___mean-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_mean___mean"><a name="math.dist.mean"></a>mean</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h6"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_mean___mean"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_mean___mean"><a name="math.dist.mean"></a>mean</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span>
<span class="identifier">RealType</span> <span class="identifier">mean</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special"><</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">>&</span> <span class="identifier">dist</span><span class="special">);</span>
@@ -312,9 +312,9 @@
if the distribution does not have a defined mean (for example the Cauchy
distribution).
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_median___median"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_median___median-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_median___median"><a name="math.dist.median"></a>median</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h7"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_median___median"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_median___median"><a name="math.dist.median"></a>median</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span>
<span class="identifier">RealType</span> <span class="identifier">median</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special"><</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">>&</span> <span class="identifier">dist</span><span class="special">);</span>
@@ -322,9 +322,9 @@
<p>
Returns the median of the distribution <span class="emphasis"><em>dist</em></span>.
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_mode___mode"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_mode___mode-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_mode___mode"><a name="math.dist.mode"></a>mode</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h8"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_mode___mode"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_mode___mode"><a name="math.dist.mode"></a>mode</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span>
<span class="identifier">RealType</span> <span class="identifier">mode</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special"><</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">>&</span> <span class="identifier">dist</span><span class="special">);</span>
@@ -336,9 +336,9 @@
This function may return a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
if the distribution does not have a defined mode.
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_pdf___probability_density_function"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_pdf___probability_density_function-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_pdf___probability_density_function"><a name="math.dist.pdf"></a>Probability Density Function</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h9"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_pdf___probability_density_function"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_pdf___probability_density_function"><a name="math.dist.pdf"></a>Probability Density Function</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span>
<span class="identifier">RealType</span> <span class="identifier">pdf</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special"><</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">>&</span> <span class="identifier">dist</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&</span> <span class="identifier">x</span><span class="special">);</span>
@@ -364,9 +364,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../graphs/pdf.png" alt="pdf"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_range___range"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_range___range-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_range___range"><a name="math.dist.range"></a>Range</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h10"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_range___range"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_range___range"><a name="math.dist.range"></a>Range</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">,</span> <span class="identifier">RealType</span><span class="special">></span> <span class="identifier">range</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special"><</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">>&</span> <span class="identifier">dist</span><span class="special">);</span>
@@ -374,9 +374,9 @@
<p>
Returns the valid range of the random variable over distribution <span class="emphasis"><em>dist</em></span>.
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_quantile___quantile"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_quantile___quantile-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_quantile___quantile"><a name="math.dist.quantile"></a>Quantile</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h11"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_quantile___quantile"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_quantile___quantile"><a name="math.dist.quantile"></a>Quantile</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span>
<span class="identifier">RealType</span> <span class="identifier">quantile</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special"><</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">>&</span> <span class="identifier">dist</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&</span> <span class="identifier">p</span><span class="special">);</span>
@@ -404,9 +404,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../graphs/quantile.png" alt="quantile"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_quantile_c___quantile_from_the_complement_of_the_probability_"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_quantile_c___quantile_from_the_complement_of_the_probability_-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_quantile_c___quantile_from_the_complement_of_the_probability_"><a name="math.dist.quantile_c"></a>Quantile from the complement of the probability.</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h12"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_quantile_c___quantile_from_the_complement_of_the_probability_"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_quantile_c___quantile_from_the_complement_of_the_probability_"><a name="math.dist.quantile_c"></a>Quantile from the complement of the probability.</a>
</h5>
<p>
<a class="link" href="../stat_tut/overview/complements.html#complements">complements</a>
@@ -449,9 +449,9 @@
<p>
<span class="inlinemediaobject"><img src="../../../../graphs/survival_inv.png" alt="survival_inv"></span>
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_sd___standard_deviation"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_sd___standard_deviation-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_sd___standard_deviation"><a name="math.dist.sd"></a>Standard Deviation</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h13"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_sd___standard_deviation"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_sd___standard_deviation"><a name="math.dist.sd"></a>Standard Deviation</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span>
<span class="identifier">RealType</span> <span class="identifier">standard_deviation</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special"><</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">>&</span> <span class="identifier">dist</span><span class="special">);</span>
@@ -463,9 +463,9 @@
This function may return a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
if the distribution does not have a defined standard deviation.
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_support___support"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_support___support-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_support___support"><a name="math.dist.support"></a>support</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h14"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_support___support"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_support___support"><a name="math.dist.support"></a>support</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">,</span> <span class="identifier">RealType</span><span class="special">></span> <span class="identifier">support</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special"><</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">>&</span> <span class="identifier">dist</span><span class="special">);</span>
@@ -480,9 +480,9 @@
that has the cdf going from zero to unity. Outside are uninteresting zones
where the pdf is zero, and the cdf zero or unity.
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_variance___variance"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_variance___variance-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_variance___variance"><a name="math.dist.variance"></a>Variance</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h15"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_variance___variance"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_variance___variance"><a name="math.dist.variance"></a>Variance</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span>
<span class="identifier">RealType</span> <span class="identifier">variance</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special"><</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">>&</span> <span class="identifier">dist</span><span class="special">);</span>
@@ -494,9 +494,9 @@
This function may return a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
if the distribution does not have a defined variance.
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_skewness___skewness"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_skewness___skewness-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_skewness___skewness"><a name="math.dist.skewness"></a>Skewness</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h16"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_skewness___skewness"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_skewness___skewness"><a name="math.dist.skewness"></a>Skewness</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span>
<span class="identifier">RealType</span> <span class="identifier">skewness</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special"><</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">>&</span> <span class="identifier">dist</span><span class="special">);</span>
@@ -508,9 +508,9 @@
This function may return a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
if the distribution does not have a defined skewness.
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_kurtosis___kurtosis"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_kurtosis___kurtosis-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_kurtosis___kurtosis"><a name="math.dist.kurtosis"></a>Kurtosis</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h17"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_kurtosis___kurtosis"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_kurtosis___kurtosis"><a name="math.dist.kurtosis"></a>Kurtosis</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span>
<span class="identifier">RealType</span> <span class="identifier">kurtosis</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special"><</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">>&</span> <span class="identifier">dist</span><span class="special">);</span>
@@ -550,9 +550,9 @@
<p>
'Proper' kurtosis can have a value from zero to + infinity.
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_kurtosis_excess___kurtosis_excess"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_kurtosis_excess___kurtosis_excess-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_kurtosis_excess___kurtosis_excess"><a name="math.dist.kurtosis_excess"></a>Kurtosis excess</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h18"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_kurtosis_excess___kurtosis_excess"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_kurtosis_excess___kurtosis_excess"><a name="math.dist.kurtosis_excess"></a>Kurtosis excess</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">></span>
<span class="identifier">RealType</span> <span class="identifier">kurtosis_excess</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special"><</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">>&</span> <span class="identifier">dist</span><span class="special">);</span>
@@ -584,9 +584,9 @@
<p>
The kurtosis excess of a normal distribution is zero.
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__cdfpq___p_and_q"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__cdfpq___p_and_q-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__cdfpq___p_and_q"><a name="cdfPQ"></a>P and Q</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h19"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__cdfpq___p_and_q"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__cdfpq___p_and_q"><a name="cdfPQ"></a>P and Q</a>
</h5>
<p>
The terms P and Q are sometimes used to refer to the <a class="link" href="nmp.html#math.dist.cdf">Cumulative
@@ -594,32 +594,32 @@
respectively. Lowercase p and q are sometimes used to refer to the values
returned by these functions.
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__percent___percent_point_function_or_percentile"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__percent___percent_point_function_or_percentile-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__percent___percent_point_function_or_percentile"><a name="percent"></a>Percent Point Function or Percentile</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h20"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__percent___percent_point_function_or_percentile"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__percent___percent_point_function_or_percentile"><a name="percent"></a>Percent Point Function or Percentile</a>
</h5>
<p>
The percent point function, also known as the percentile, is the same as
the <a class="link" href="nmp.html#math.dist.quantile">Quantile</a>.
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__cdf_inv___inverse_cdf_function_"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__cdf_inv___inverse_cdf_function_-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__cdf_inv___inverse_cdf_function_"><a name="cdf_inv"></a>Inverse CDF Function.</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h21"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__cdf_inv___inverse_cdf_function_"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__cdf_inv___inverse_cdf_function_"><a name="cdf_inv"></a>Inverse CDF Function.</a>
</h5>
<p>
The inverse of the cumulative distribution function, is the same as the
<a class="link" href="nmp.html#math.dist.quantile">Quantile</a>.
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__survival_inv___inverse_survival_function_"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__survival_inv___inverse_survival_function_-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__survival_inv___inverse_survival_function_"><a name="survival_inv"></a>Inverse Survival Function.</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h22"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__survival_inv___inverse_survival_function_"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__survival_inv___inverse_survival_function_"><a name="survival_inv"></a>Inverse Survival Function.</a>
</h5>
<p>
The inverse of the survival function, is the same as computing the <a class="link" href="nmp.html#math.dist.quantile_c">quantile from the complement of the probability</a>.
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__pmf___probability_mass_function"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__pmf___probability_mass_function-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__pmf___probability_mass_function"><a name="pmf"></a>Probability Mass Function</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h23"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__pmf___probability_mass_function"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__pmf___probability_mass_function"><a name="pmf"></a>Probability Mass Function</a>
</h5>
<p>
The Probability Mass Function is the same as the <a class="link" href="nmp.html#math.dist.pdf">Probability
@@ -630,18 +630,18 @@
the term <a class="link" href="nmp.html#math.dist.pdf">Probability Density Function</a>
applies to continuous distributions.
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__lower_critical___lower_critical_value_"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__lower_critical___lower_critical_value_-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__lower_critical___lower_critical_value_"><a name="lower_critical"></a>Lower Critical Value.</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h24"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__lower_critical___lower_critical_value_"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__lower_critical___lower_critical_value_"><a name="lower_critical"></a>Lower Critical Value.</a>
</h5>
<p>
The lower critical value calculates the value of the random variable given
the area under the left tail of the distribution. It is equivalent to calculating
the <a class="link" href="nmp.html#math.dist.quantile">Quantile</a>.
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__upper_critical___upper_critical_value_"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__upper_critical___upper_critical_value_-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__upper_critical___upper_critical_value_"><a name="upper_critical"></a>Upper Critical Value.</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h25"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__upper_critical___upper_critical_value_"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__upper_critical___upper_critical_value_"><a name="upper_critical"></a>Upper Critical Value.</a>
</h5>
<p>
The upper critical value calculates the value of the random variable given
@@ -649,9 +649,9 @@
calculating the <a class="link" href="nmp.html#math.dist.quantile_c">quantile from the
complement of the probability</a>.
</p>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__survival___survival_function"></a><h5>
-<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__survival___survival_function-heading"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__survival___survival_function"><a name="survival"></a>Survival Function</a>
+<h5>
+<a name="math_toolkit.dist.dist_ref.nmp.h26"></a>
+ <span><a name="math_toolkit.dist.dist_ref.nmp._anchor_id__survival___survival_function"></a></span><a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__survival___survival_function"><a name="survival"></a>Survival Function</a>
</h5>
<p>
Refer to the <a class="link" href="nmp.html#math.dist.ccdf">Complement of the Cumulative
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/future.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/future.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/future.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -26,9 +26,9 @@
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.dist.future"></a><a class="link" href="future.html" title="Extras/Future Directions">Extras/Future Directions</a>
</h3></div></div></div>
-<a name="math_toolkit.dist.future.adding_additional_location_and_scale_parameters"></a><h5>
-<a name="math_toolkit.dist.future.adding_additional_location_and_scale_parameters-heading"></a>
- <a class="link" href="future.html#math_toolkit.dist.future.adding_additional_location_and_scale_parameters">Adding
+<h5>
+<a name="math_toolkit.dist.future.h0"></a>
+ <span><a name="math_toolkit.dist.future.adding_additional_location_and_scale_parameters"></a></span><a class="link" href="future.html#math_toolkit.dist.future.adding_additional_location_and_scale_parameters">Adding
Additional Location and Scale Parameters</a>
</h5>
<p>
@@ -45,7 +45,7 @@
<span class="keyword">class</span> <span class="identifier">scaled_distribution</span>
<span class="special">{</span>
<span class="identifier">scaled_distribution</span><span class="special">(</span>
- <span class="keyword">const</span> <span class="identifier">Dist</span> <span class="identifier">dist</span><span class="special">,</span>
+ <span class="keyword">const</span> <span class="identifier">Dist</span> <span class="identifier">dist</span><span class="special">,</span>
<span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">location</span><span class="special">,</span>
<span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">0</span><span class="special">);</span>
<span class="special">};</span>
@@ -54,9 +54,9 @@
Which would then have its own set of overloads for the non-member accessor
functions.
</p>
-<a name="math_toolkit.dist.future.an__quot_any_distribution_quot__class"></a><h5>
-<a name="math_toolkit.dist.future.an__quot_any_distribution_quot__class-heading"></a>
- <a class="link" href="future.html#math_toolkit.dist.future.an__quot_any_distribution_quot__class">An
+<h5>
+<a name="math_toolkit.dist.future.h1"></a>
+ <span><a name="math_toolkit.dist.future.an__quot_any_distribution_quot__class"></a></span><a class="link" href="future.html#math_toolkit.dist.future.an__quot_any_distribution_quot__class">An
"any_distribution" class</a>
</h5>
<p>
@@ -90,10 +90,10 @@
tests for goodness of fit might provide such a use case: this needs more
investigation.
</p>
-<a name="math_toolkit.dist.future.higher_level_hypothesis_tests"></a><h5>
-<a name="math_toolkit.dist.future.higher_level_hypothesis_tests-heading"></a>
- <a class="link" href="future.html#math_toolkit.dist.future.higher_level_hypothesis_tests">Higher
- Level Hypothesis Tests</a>
+<h5>
+<a name="math_toolkit.dist.future.h2"></a>
+ <span><a name="math_toolkit.dist.future.higher_level_hypothesis_tests"></a></span><a class="link" href="future.html#math_toolkit.dist.future.higher_level_hypothesis_tests">Higher Level
+ Hypothesis Tests</a>
</h5>
<p>
Higher-level tests roughly corresponding to the <a href="http://documents.wolfram.com/mathematica/Add-onsLinks/StandardPackages/Statistics/HypothesisTests.html" target="_top">Mathematica
@@ -110,9 +110,9 @@
Returns the probability that the data in the sequence [a,b) has the mean
<span class="emphasis"><em>expected_mean</em></span>.
</p>
-<a name="math_toolkit.dist.future.integration_with_statistical_accumulators"></a><h5>
-<a name="math_toolkit.dist.future.integration_with_statistical_accumulators-heading"></a>
- <a class="link" href="future.html#math_toolkit.dist.future.integration_with_statistical_accumulators">Integration
+<h5>
+<a name="math_toolkit.dist.future.h3"></a>
+ <span><a name="math_toolkit.dist.future.integration_with_statistical_accumulators"></a></span><a class="link" href="future.html#math_toolkit.dist.future.integration_with_statistical_accumulators">Integration
With Statistical Accumulators</a>
</h5>
<p>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -145,10 +145,10 @@
<span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">fixed</span> <span class="special"><<</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">5</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">15</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">right</span> <span class="special"><<</span> <span class="identifier">u</span><span class="special">;</span>
<span class="comment">// Calculate Jeffreys Prior Bounds:</span>
<span class="identifier">l</span> <span class="special">=</span> <span class="identifier">binomial_distribution</span><span class="special"><>::</span><span class="identifier">find_lower_bound_on_p</span><span class="special">(</span>
- <span class="identifier">trials</span><span class="special">,</span> <span class="identifier">successes</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]/</span><span class="number">2</span><span class="special">,</span>
+ <span class="identifier">trials</span><span class="special">,</span> <span class="identifier">successes</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]/</span><span class="number">2</span><span class="special">,</span>
<span class="identifier">binomial_distribution</span><span class="special"><>::</span><span class="identifier">jeffreys_prior_interval</span><span class="special">);</span>
<span class="identifier">u</span> <span class="special">=</span> <span class="identifier">binomial_distribution</span><span class="special"><>::</span><span class="identifier">find_upper_bound_on_p</span><span class="special">(</span>
- <span class="identifier">trials</span><span class="special">,</span> <span class="identifier">successes</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]/</span><span class="number">2</span><span class="special">,</span>
+ <span class="identifier">trials</span><span class="special">,</span> <span class="identifier">successes</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]/</span><span class="number">2</span><span class="special">,</span>
<span class="identifier">binomial_distribution</span><span class="special"><>::</span><span class="identifier">jeffreys_prior_interval</span><span class="special">);</span>
<span class="comment">// Print Jeffreys Prior Limits:</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">fixed</span> <span class="special"><<</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">5</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">15</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">right</span> <span class="special"><<</span> <span class="identifier">l</span><span class="special">;</span>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -53,7 +53,6 @@
the binomial distribution, some std input and output, and get started:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">binomial</span><span class="special">;</span>
@@ -79,7 +78,6 @@
1/2, and how many flips.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">const</span> <span class="keyword">double</span> <span class="identifier">success_fraction</span> <span class="special">=</span> <span class="number">0.5</span><span class="special">;</span> <span class="comment">// = 50% = 1/2 for a 'fair' coin.</span>
<span class="keyword">int</span> <span class="identifier">flips</span> <span class="special">=</span> <span class="number">10</span><span class="special">;</span>
@@ -92,7 +90,6 @@
Then some examples of using Binomial moments (and echoing the parameters).
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"From "</span> <span class="special"><<</span> <span class="identifier">flips</span> <span class="special"><<</span> <span class="string">" one can expect to get on average "</span>
<span class="special"><<</span> <span class="identifier">mean</span><span class="special">(</span><span class="identifier">flip</span><span class="special">)</span> <span class="special"><<</span> <span class="string">" heads (or tails)."</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
@@ -113,7 +110,6 @@
Now we show a variety of predictions on the probability of heads:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"For "</span> <span class="special"><<</span> <span class="identifier">flip</span><span class="special">.</span><span class="identifier">trials</span><span class="special">()</span> <span class="special"><<</span> <span class="string">" coin flips: "</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of getting no heads is "</span> <span class="special"><<</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">0</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
@@ -125,7 +121,6 @@
can sum the PDF's:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of getting 0 or 1 heads is "</span>
<span class="special"><<</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">0</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">1</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// sum of exactly == probabilities</span></pre>
@@ -135,7 +130,6 @@
Or we can use the cdf.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of getting 0 or 1 (<= 1) heads is "</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">1</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of getting 9 or 10 heads is "</span> <span class="special"><<</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">9</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">10</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span></pre>
@@ -145,7 +139,6 @@
Note that using
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of getting 9 or 10 heads is "</span> <span class="special"><<</span> <span class="number">1.</span> <span class="special">-</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">8</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span></pre>
<p>
@@ -154,7 +147,6 @@
is less accurate than using the complement
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of getting 9 or 10 heads is "</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">8</span><span class="special">))</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span></pre>
<p>
@@ -170,7 +162,6 @@
pdfs for each number of heads
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of between 4 and 6 heads (4 or 5 or 6) is "</span>
<span class="comment">// P(X == 4) + P(X == 5) + P(X == 6)</span>
@@ -181,7 +172,6 @@
But this is probably less efficient than using the cdf
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of between 4 and 6 heads (4 or 5 or 6) is "</span>
<span class="comment">// P(X <= 6) - P(X <= 3) == P(X < 4)</span>
@@ -192,7 +182,6 @@
Certainly for a bigger range like, 3 to 7
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of between 3 and 7 heads (3, 4, 5, 6 or 7) is "</span>
<span class="comment">// P(X <= 7) - P(X <= 2) == P(X < 3)</span>
@@ -205,7 +194,6 @@
and <span class="emphasis"><em>at least</em></span> a number of heads.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="comment">// Print a table of probability for the exactly a number of heads.</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of getting exactly (==) heads"</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
@@ -234,7 +222,6 @@
The last (0 to 10 heads) must, of course, be 100% probability.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="special">}</span>
<span class="keyword">catch</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exception</span><span class="special">&</span> <span class="identifier">e</span><span class="special">)</span>
@@ -253,7 +240,6 @@
as to the cause of the problem.
</p>
<p>
-
</p>
<pre class="programlisting"> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span>
<span class="string">"\n"</span><span class="string">"Message from thrown exception was:\n "</span> <span class="special"><<</span> <span class="identifier">e</span><span class="special">.</span><span class="identifier">what</span><span class="special">()</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -44,7 +44,6 @@
(and some std input/output, of course).
</p>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">binomial</span><span class="special">;</span>
@@ -67,7 +66,6 @@
fraction probability p. So we construct a binomial distribution:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">questions</span> <span class="special">=</span> <span class="number">16</span><span class="special">;</span> <span class="comment">// All the questions in the quiz.</span>
<span class="keyword">int</span> <span class="identifier">answers</span> <span class="special">=</span> <span class="number">4</span><span class="special">;</span> <span class="comment">// Possible answers to each question.</span>
@@ -79,7 +77,6 @@
and display the distribution parameters we used thus:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"In a quiz with "</span> <span class="special"><<</span> <span class="identifier">quiz</span><span class="special">.</span><span class="identifier">trials</span><span class="special">()</span>
<span class="special"><<</span> <span class="string">" questions and with a probability of guessing right of "</span>
@@ -91,7 +88,6 @@
Show a few probabilities of just guessing:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of getting none right is "</span> <span class="special"><<</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.010023</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of getting exactly one right is "</span> <span class="special"><<</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">1</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
@@ -116,7 +112,6 @@
We can tabulate the 'getting exactly right' ( == ) probabilities thus:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"\n"</span> <span class="string">"Guessed Probability"</span> <span class="special"><<</span> <span class="identifier">right</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">for</span> <span class="special">(</span><span class="keyword">int</span> <span class="identifier">successes</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">successes</span> <span class="special"><=</span> <span class="identifier">questions</span><span class="special">;</span> <span class="identifier">successes</span><span class="special">++)</span>
@@ -150,7 +145,6 @@
Then we can add the probabilities of some 'exactly right' like this:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of getting none or one right is "</span> <span class="special"><<</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">1</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span></pre>
<p>
@@ -163,7 +157,6 @@
(cdf) instead:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of getting none or one right is "</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">1</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span></pre>
<p>
@@ -175,7 +168,6 @@
to 10 right ( <= )
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of getting <= 10 right (to fail) is "</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">10</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span></pre>
<p>
@@ -184,14 +176,13 @@
</pre>
<p>
To get the probability of getting 11 or more right (to pass), it is
- tempting to use
+ tempting to use
</p>
<pre class="programlisting"><span class="number">1</span> <span class="special">-</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">10</span><span class="special">)</span></pre>
<p>
to get the probability of > 10
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of getting > 10 right (to pass) is "</span> <span class="special"><<</span> <span class="number">1</span> <span class="special">-</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">10</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span></pre>
<p>
@@ -203,7 +194,6 @@
<a class="link" href="../../overview/complements.html#why_complements">Why complements?</a>
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of getting > 10 right (to pass) is "</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">10</span><span class="special">))</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span></pre>
<p>
@@ -214,7 +204,6 @@
And we can check that these two, <= 10 and > 10, add up to unity.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">BOOST_ASSERT</span><span class="special">((</span><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">10</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">10</span><span class="special">)))</span> <span class="special">==</span> <span class="number">1.</span><span class="special">);</span></pre>
<p>
@@ -224,7 +213,6 @@
we must subtract one from the score.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of getting less than "</span> <span class="special"><<</span> <span class="identifier">pass_score</span>
<span class="special"><<</span> <span class="string">" (< "</span> <span class="special"><<</span> <span class="identifier">pass_score</span> <span class="special"><<</span> <span class="string">") answers right by guessing is "</span>
@@ -241,7 +229,6 @@
would be one possible outcome counted twice!
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of getting at least "</span> <span class="special"><<</span> <span class="identifier">pass_score</span>
<span class="special"><<</span> <span class="string">"(>= "</span> <span class="special"><<</span> <span class="identifier">pass_score</span> <span class="special"><<</span> <span class="string">") answers right by guessing is "</span>
@@ -257,7 +244,6 @@
Finally we can tabulate some probabilities:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"\n"</span> <span class="string">"At most (<=)"</span><span class="string">"\n"</span><span class="string">"Guessed OK Probability"</span> <span class="special"><<</span> <span class="identifier">right</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">for</span> <span class="special">(</span><span class="keyword">int</span> <span class="identifier">score</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">score</span> <span class="special"><=</span> <span class="identifier">questions</span><span class="special">;</span> <span class="identifier">score</span><span class="special">++)</span>
@@ -289,7 +275,6 @@
16 1
</pre>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"\n"</span> <span class="string">"At least (>)"</span><span class="string">"\n"</span><span class="string">"Guessed OK Probability"</span> <span class="special"><<</span> <span class="identifier">right</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">for</span> <span class="special">(</span><span class="keyword">int</span> <span class="identifier">score</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">score</span> <span class="special"><=</span> <span class="identifier">questions</span><span class="special">;</span> <span class="identifier">score</span><span class="special">++)</span>
@@ -328,7 +313,6 @@
by adding the exact probabilities of each from low ... high.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">low</span> <span class="special">=</span> <span class="number">3</span><span class="special">;</span> <span class="comment">// Getting at least 3 right.</span>
<span class="keyword">int</span> <span class="identifier">high</span> <span class="special">=</span> <span class="number">5</span><span class="special">;</span> <span class="comment">// Getting as most 5 right.</span>
@@ -349,7 +333,6 @@
Or, usually better, we can use the difference of cdfs instead:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of getting between "</span> <span class="special"><<</span> <span class="identifier">low</span> <span class="special"><<</span> <span class="string">" and "</span> <span class="special"><<</span> <span class="identifier">high</span> <span class="special"><<</span> <span class="string">" answers right by guessing is "</span>
<span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="identifier">high</span><span class="special">)</span> <span class="special">-</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="identifier">low</span> <span class="special">-</span> <span class="number">1</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.61323</span></pre>
@@ -361,7 +344,6 @@
And we can also try a few more combinations of high and low choices:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">low</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> <span class="identifier">high</span> <span class="special">=</span> <span class="number">6</span><span class="special">;</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of getting between "</span> <span class="special"><<</span> <span class="identifier">low</span> <span class="special"><<</span> <span class="string">" and "</span> <span class="special"><<</span> <span class="identifier">high</span> <span class="special"><<</span> <span class="string">" answers right by guessing is "</span>
@@ -378,9 +360,9 @@
Probability of getting between 1 and 8 answers right by guessing is 0.9825
Probability of getting between 4 and 4 answers right by guessing is 0.2252
</pre>
-<a name="math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.using_binomial_distribution_moments"></a><h5>
-<a name="math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.using_binomial_distribution_moments-heading"></a>
- <a class="link" href="binomial_quiz_example.html#math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.using_binomial_distribution_moments">Using
+<h5>
+<a name="math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.h0"></a>
+ <span><a name="math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.using_binomial_distribution_moments"></a></span><a class="link" href="binomial_quiz_example.html#math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.using_binomial_distribution_moments">Using
Binomial distribution moments</a>
</h5>
<p>
@@ -388,7 +370,6 @@
of results from guessing.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"By guessing, on average, one can expect to get "</span> <span class="special"><<</span> <span class="identifier">mean</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">)</span> <span class="special"><<</span> <span class="string">" correct answers."</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Standard deviation is "</span> <span class="special"><<</span> <span class="identifier">standard_deviation</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
@@ -405,16 +386,15 @@
Mode (the most frequent) is 4
Skewness is 0.2887
</pre>
-<a name="math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.quantiles"></a><h5>
-<a name="math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.quantiles-heading"></a>
- <a class="link" href="binomial_quiz_example.html#math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.quantiles">Quantiles</a>
+<h5>
+<a name="math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.h1"></a>
+ <span><a name="math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.quantiles"></a></span><a class="link" href="binomial_quiz_example.html#math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.quantiles">Quantiles</a>
</h5>
<p>
The quantiles (percentiles or percentage points) for a few probability
levels:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Quartiles "</span> <span class="special"><<</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0.25</span><span class="special">)</span> <span class="special"><<</span> <span class="string">" to "</span>
<span class="special"><<</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0.25</span><span class="special">))</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// Quartiles</span>
@@ -472,7 +452,6 @@
real (here avoiding any 'using namespaces ...' statements):
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">discrete_quantile</span><span class="special">;</span>
@@ -482,17 +461,16 @@
<p>
</p>
<p>
- Add a custom binomial distribution called
+ Add a custom binomial distribution called
</p>
<pre class="programlisting"><span class="identifier">real_quantile_binomial</span></pre>
<p>
- that uses
+ that uses
</p>
<pre class="programlisting"><span class="identifier">real_quantile_policy</span></pre>
<p>
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">binomial_distribution</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">binomial_distribution</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">real_quantile_policy</span><span class="special">></span> <span class="identifier">real_quantile_binomial</span><span class="special">;</span></pre>
@@ -502,7 +480,6 @@
Construct an object of this custom distribution:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">real_quantile_binomial</span> <span class="identifier">quiz_real</span><span class="special">(</span><span class="identifier">questions</span><span class="special">,</span> <span class="identifier">success_fraction</span><span class="special">);</span></pre>
<p>
@@ -512,7 +489,6 @@
integer values.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Quartiles "</span> <span class="special"><<</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0.25</span><span class="special">)</span> <span class="special"><<</span> <span class="string">" to "</span>
<span class="special"><<</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz_real</span><span class="special">,</span> <span class="number">0.25</span><span class="special">))</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// Quartiles 2 to 4.6212</span>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -138,9 +138,9 @@
So at the 95% confidence level we conclude that the standard deviation
is between 0.00551 and 0.00729.
</p>
-<a name="math_toolkit.dist.stat_tut.weg.cs_eg.chi_sq_intervals.confidence_intervals_as_a_function_of_the_number_of_observations"></a><h5>
-<a name="math_toolkit.dist.stat_tut.weg.cs_eg.chi_sq_intervals.confidence_intervals_as_a_function_of_the_number_of_observations-heading"></a>
- <a class="link" href="chi_sq_intervals.html#math_toolkit.dist.stat_tut.weg.cs_eg.chi_sq_intervals.confidence_intervals_as_a_function_of_the_number_of_observations">Confidence
+<h5>
+<a name="math_toolkit.dist.stat_tut.weg.cs_eg.chi_sq_intervals.h0"></a>
+ <span><a name="math_toolkit.dist.stat_tut.weg.cs_eg.chi_sq_intervals.confidence_intervals_as_a_function_of_the_number_of_observations"></a></span><a class="link" href="chi_sq_intervals.html#math_toolkit.dist.stat_tut.weg.cs_eg.chi_sq_intervals.confidence_intervals_as_a_function_of_the_number_of_observations">Confidence
intervals as a function of the number of observations</a>
</h5>
<p>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -45,7 +45,6 @@
(and the binomial, beta and gamma too).
</p>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">negative_binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> <span class="comment">// for negative_binomial_distribution</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">negative_binomial_distribution</span><span class="special">;</span> <span class="comment">// default type is double.</span>
@@ -64,7 +63,6 @@
fraction 0.25, 25% or 1 in 4, is constructed like this:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">negative_binomial_distribution</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">mydist0</span><span class="special">(</span><span class="number">8.</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span></pre>
<p>
@@ -73,7 +71,6 @@
But this is inconveniently long, so we might be tempted to write
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span></pre>
<p>
@@ -83,7 +80,6 @@
is explicit <code class="computeroutput"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span> </code> * ... statements like
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">negative_binomial_distribution</span><span class="special">;</span></pre>
<p>
@@ -97,7 +93,6 @@
double, so we can also write:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">negative_binomial_distribution</span><span class="special"><></span> <span class="identifier">mydist9</span><span class="special">(</span><span class="number">8.</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span> <span class="comment">// Uses default RealType = double.</span></pre>
<p>
@@ -124,7 +119,6 @@
So, after a using statement,
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">negative_binomial</span><span class="special">;</span></pre>
<p>
@@ -133,7 +127,6 @@
we have a convenient typedef to <code class="computeroutput"><span class="identifier">negative_binomial_distribution</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span></code>:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">negative_binomial</span> <span class="identifier">mydist</span><span class="special">(</span><span class="number">8.</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span></pre>
<p>
@@ -142,7 +135,6 @@
Some more examples using the convenience typedef:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">negative_binomial</span> <span class="identifier">mydist10</span><span class="special">(</span><span class="number">5.</span><span class="special">,</span> <span class="number">0.4</span><span class="special">);</span> <span class="comment">// Both arguments double.</span></pre>
<p>
@@ -151,7 +143,6 @@
And automatic conversion takes place, so you can use integers and floats:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">negative_binomial</span> <span class="identifier">mydist11</span><span class="special">(</span><span class="number">5</span><span class="special">,</span> <span class="number">0.4</span><span class="special">);</span> <span class="comment">// Using provided typedef double, int and double arguments.</span></pre>
<p>
@@ -160,7 +151,6 @@
This is probably the most common usage.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">negative_binomial</span> <span class="identifier">mydist12</span><span class="special">(</span><span class="number">5.</span><span class="special">,</span> <span class="number">0.4F</span><span class="special">);</span> <span class="comment">// Double and float arguments.</span>
<span class="identifier">negative_binomial</span> <span class="identifier">mydist13</span><span class="special">(</span><span class="number">5</span><span class="special">,</span> <span class="number">1</span><span class="special">);</span> <span class="comment">// Both arguments integer.</span></pre>
@@ -170,7 +160,6 @@
Similarly for most other distributions like the binomial.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">binomial</span> <span class="identifier">mybinomial</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="number">0.5</span><span class="special">);</span> <span class="comment">// is more concise than</span>
<span class="identifier">binomial_distribution</span><span class="special"><></span> <span class="identifier">mybinomd1</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="number">0.5</span><span class="special">);</span></pre>
@@ -196,7 +185,6 @@
Instead you should use:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">beta_distribution</span><span class="special">;</span>
<span class="identifier">beta_distribution</span><span class="special"><></span> <span class="identifier">mybetad1</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="number">0.5</span><span class="special">);</span></pre>
@@ -206,7 +194,6 @@
or for the gamma distribution:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">gamma_distribution</span><span class="special"><></span> <span class="identifier">mygammad1</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="number">0.5</span><span class="special">);</span></pre>
<p>
@@ -215,7 +202,6 @@
We can, of course, still provide the type explicitly thus:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="comment">// Explicit double precision:</span>
<span class="identifier">negative_binomial_distribution</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">mydist1</span><span class="special">(</span><span class="number">8.</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span>
@@ -245,9 +231,9 @@
</p>
<pre class="programlisting"><span class="identifier">negative_binomial_distribution</span><span class="special"><</span><span class="identifier">MyFPType</span><span class="special">></span> <span class="identifier">mydist6</span><span class="special">(</span><span class="number">8</span><span class="special">,</span> <span class="number">1</span><span class="special">);</span> <span class="comment">// Integer arguments -> MyFPType.</span>
</pre>
-<a name="math_toolkit.dist.stat_tut.weg.dist_construct_eg.default_arguments_to_distribution_constructors_"></a><h6>
-<a name="math_toolkit.dist.stat_tut.weg.dist_construct_eg.default_arguments_to_distribution_constructors_-heading"></a>
- <a class="link" href="dist_construct_eg.html#math_toolkit.dist.stat_tut.weg.dist_construct_eg.default_arguments_to_distribution_constructors_">Default
+<h6>
+<a name="math_toolkit.dist.stat_tut.weg.dist_construct_eg.h0"></a>
+ <span><a name="math_toolkit.dist.stat_tut.weg.dist_construct_eg.default_arguments_to_distribution_constructors_"></a></span><a class="link" href="dist_construct_eg.html#math_toolkit.dist.stat_tut.weg.dist_construct_eg.default_arguments_to_distribution_constructors_">Default
arguments to distribution constructors.</a>
</h6>
<p>
@@ -271,7 +257,6 @@
So in this case we can write:
</p>
<p>
-
</p>
<pre class="programlisting"> <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">normal</span><span class="special">;</span>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -79,7 +79,6 @@
We'll begin our sample program with the needed includes:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="comment">// Boost</span>
<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">students_t</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
@@ -103,7 +102,6 @@
handle either an exception or a NaN:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
<span class="special">{</span>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -32,7 +32,6 @@
algorithms to find location (and some std output of course).
</p>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> <span class="comment">// for normal_distribution</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">normal</span><span class="special">;</span> <span class="comment">// typedef provides default type is double.</span>
@@ -61,7 +60,6 @@
also the default for this implementation.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">normal</span> <span class="identifier">N01</span><span class="special">;</span> <span class="comment">// Default 'standard' normal distribution with zero mean and </span>
<span class="keyword">double</span> <span class="identifier">sd</span> <span class="special">=</span> <span class="number">1.</span><span class="special">;</span> <span class="comment">// normal default standard deviation is 1.</span></pre>
@@ -73,14 +71,13 @@
certain chosen limit (here -2, two standard deviations).
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">z</span> <span class="special">=</span> <span class="special">-</span><span class="number">2.</span><span class="special">;</span> <span class="comment">// z to give prob p</span>
<span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="number">0.001</span><span class="special">;</span> <span class="comment">// only 0.1% below z</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Normal distribution with mean = "</span> <span class="special"><<</span> <span class="identifier">N01</span><span class="special">.</span><span class="identifier">location</span><span class="special">()</span>
<span class="special"><<</span> <span class="string">", standard deviation "</span> <span class="special"><<</span> <span class="identifier">N01</span><span class="special">.</span><span class="identifier">scale</span><span class="special">()</span>
- <span class="special"><<</span> <span class="string">", has "</span> <span class="special"><<</span> <span class="string">"fraction <= "</span> <span class="special"><<</span> <span class="identifier">z</span>
+ <span class="special"><<</span> <span class="string">", has "</span> <span class="special"><<</span> <span class="string">"fraction <= "</span> <span class="special"><<</span> <span class="identifier">z</span>
<span class="special"><<</span> <span class="string">", p = "</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">N01</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Normal distribution with mean = "</span> <span class="special"><<</span> <span class="identifier">N01</span><span class="special">.</span><span class="identifier">location</span><span class="special">()</span>
<span class="special"><<</span> <span class="string">", standard deviation "</span> <span class="special"><<</span> <span class="identifier">N01</span><span class="special">.</span><span class="identifier">scale</span><span class="special">()</span>
@@ -95,7 +92,6 @@
We can now use ''find_location'' to give a new offset mean.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">l</span> <span class="special">=</span> <span class="identifier">find_location</span><span class="special"><</span><span class="identifier">normal</span><span class="special">>(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">sd</span><span class="special">);</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"offset location (mean) = "</span> <span class="special"><<</span> <span class="identifier">l</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span></pre>
@@ -115,7 +111,6 @@
a new distribution with the offset mean (but same standard deviation):
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">normal</span> <span class="identifier">np001pc</span><span class="special">(</span><span class="identifier">l</span><span class="special">,</span> <span class="identifier">sd</span><span class="special">);</span> <span class="comment">// Same standard_deviation (scale) but with mean (location) shifted.</span></pre>
<p>
@@ -124,22 +119,21 @@
And re-calculating the fraction below our chosen limit.
</p>
<p>
-
</p>
-<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Normal distribution with mean = "</span> <span class="special"><<</span> <span class="identifier">l</span>
- <span class="special"><<</span> <span class="string">" has "</span> <span class="special"><<</span> <span class="string">"fraction <= "</span> <span class="special"><<</span> <span class="identifier">z</span>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Normal distribution with mean = "</span> <span class="special"><<</span> <span class="identifier">l</span>
+ <span class="special"><<</span> <span class="string">" has "</span> <span class="special"><<</span> <span class="string">"fraction <= "</span> <span class="special"><<</span> <span class="identifier">z</span>
<span class="special"><<</span> <span class="string">", p = "</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">np001pc</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
- <span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Normal distribution with mean = "</span> <span class="special"><<</span> <span class="identifier">l</span>
- <span class="special"><<</span> <span class="string">" has "</span> <span class="special"><<</span> <span class="string">"fraction > "</span> <span class="special"><<</span> <span class="identifier">z</span>
+ <span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Normal distribution with mean = "</span> <span class="special"><<</span> <span class="identifier">l</span>
+ <span class="special"><<</span> <span class="string">" has "</span> <span class="special"><<</span> <span class="string">"fraction > "</span> <span class="special"><<</span> <span class="identifier">z</span>
<span class="special"><<</span> <span class="string">", p = "</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">np001pc</span><span class="special">,</span> <span class="identifier">z</span><span class="special">))</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span></pre>
<p>
</p>
<pre class="programlisting">Normal distribution with mean = 1.09023 has fraction <= -2, p = 0.001
Normal distribution with mean = 1.09023 has fraction > -2, p = 0.999
</pre>
-<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_location_eg.controlling_error_handling_from_find_location"></a><h5>
-<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_location_eg.controlling_error_handling_from_find_location-heading"></a>
- <a class="link" href="find_location_eg.html#math_toolkit.dist.stat_tut.weg.find_eg.find_location_eg.controlling_error_handling_from_find_location">Controlling
+<h5>
+<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_location_eg.h0"></a>
+ <span><a name="math_toolkit.dist.stat_tut.weg.find_eg.find_location_eg.controlling_error_handling_from_find_location"></a></span><a class="link" href="find_location_eg.html#math_toolkit.dist.stat_tut.weg.find_eg.find_location_eg.controlling_error_handling_from_find_location">Controlling
Error Handling from find_location</a>
</h5>
<p>
@@ -151,7 +145,6 @@
Unless we are using the boost::math namespace, we will need:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">domain_error</span><span class="special">;</span>
@@ -163,7 +156,6 @@
it is not required, as the various examples below show.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special"><</span><span class="identifier">domain_error</span><span class="special"><</span><span class="identifier">ignore_error</span><span class="special">></span> <span class="special">></span> <span class="identifier">ignore_domain_policy</span><span class="special">;</span>
<span class="comment">// find_location with new policy, using typedef.</span>
@@ -183,16 +175,15 @@
use the complement version.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">z</span> <span class="special">=</span> <span class="number">2.</span><span class="special">;</span>
<span class="keyword">double</span> <span class="identifier">q</span> <span class="special">=</span> <span class="number">0.95</span><span class="special">;</span> <span class="comment">// = 1 - p; // complement.</span>
<span class="identifier">l</span> <span class="special">=</span> <span class="identifier">find_location</span><span class="special"><</span><span class="identifier">normal</span><span class="special">>(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">q</span><span class="special">,</span> <span class="identifier">sd</span><span class="special">));</span>
<span class="identifier">normal</span> <span class="identifier">np95pc</span><span class="special">(</span><span class="identifier">l</span><span class="special">,</span> <span class="identifier">sd</span><span class="special">);</span> <span class="comment">// Same standard_deviation (scale) but with mean(location) shifted</span>
-<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Normal distribution with mean = "</span> <span class="special"><<</span> <span class="identifier">l</span> <span class="special"><<</span> <span class="string">" has "</span>
+<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Normal distribution with mean = "</span> <span class="special"><<</span> <span class="identifier">l</span> <span class="special"><<</span> <span class="string">" has "</span>
<span class="special"><<</span> <span class="string">"fraction <= "</span> <span class="special"><<</span> <span class="identifier">z</span> <span class="special"><<</span> <span class="string">" = "</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">np95pc</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
-<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Normal distribution with mean = "</span> <span class="special"><<</span> <span class="identifier">l</span> <span class="special"><<</span> <span class="string">" has "</span>
+<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Normal distribution with mean = "</span> <span class="special"><<</span> <span class="identifier">l</span> <span class="special"><<</span> <span class="string">" has "</span>
<span class="special"><<</span> <span class="string">"fraction > "</span> <span class="special"><<</span> <span class="identifier">z</span> <span class="special"><<</span> <span class="string">" = "</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">np95pc</span><span class="special">,</span> <span class="identifier">z</span><span class="special">))</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
</pre>
<p>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -32,7 +32,6 @@
algorithms to find location and scale (and some std output of course).
</p>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> <span class="comment">// for normal_distribution</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">normal</span><span class="special">;</span> <span class="comment">// typedef provides default type is double.</span>
@@ -56,9 +55,9 @@
</pre>
<p>
</p>
-<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.using_find_location_and_find_scale_to_meet_dispensing_and_measurement_specifications"></a><h5>
-<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.using_find_location_and_find_scale_to_meet_dispensing_and_measurement_specifications-heading"></a>
- <a class="link" href="find_mean_and_sd_eg.html#math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.using_find_location_and_find_scale_to_meet_dispensing_and_measurement_specifications">Using
+<h5>
+<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.h0"></a>
+ <span><a name="math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.using_find_location_and_find_scale_to_meet_dispensing_and_measurement_specifications"></a></span><a class="link" href="find_mean_and_sd_eg.html#math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.using_find_location_and_find_scale_to_meet_dispensing_and_measurement_specifications">Using
find_location and find_scale to meet dispensing and measurement specifications</a>
</h5>
<p>
@@ -75,7 +74,6 @@
We start by constructing a normal distribution with the given parameters:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">mean</span> <span class="special">=</span> <span class="number">3.</span><span class="special">;</span> <span class="comment">// kg</span>
<span class="keyword">double</span> <span class="identifier">standard_deviation</span> <span class="special">=</span> <span class="number">0.1</span><span class="special">;</span> <span class="comment">// kg</span>
@@ -87,7 +85,6 @@
3.1 kg.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">max_weight</span> <span class="special">=</span> <span class="number">3.1</span><span class="special">;</span> <span class="comment">// kg</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Percentage of packs > "</span> <span class="special"><<</span> <span class="identifier">max_weight</span> <span class="special"><<</span> <span class="string">" is "</span>
@@ -104,7 +101,6 @@
fail to meet the specification of 2.9 kg.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">minimum_weight</span> <span class="special">=</span> <span class="number">2.9</span><span class="special">;</span>
<span class="identifier">cout</span> <span class="special"><<</span><span class="string">"Fraction of packs <= "</span> <span class="special"><<</span> <span class="identifier">minimum_weight</span> <span class="special"><<</span> <span class="string">" with a mean of "</span> <span class="special"><<</span> <span class="identifier">mean</span>
@@ -126,7 +122,6 @@
'xpacks' with a safety margin mean of 3.06449 thus:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">over_mean</span> <span class="special">=</span> <span class="number">3.06449</span><span class="special">;</span>
<span class="identifier">normal</span> <span class="identifier">xpacks</span><span class="special">(</span><span class="identifier">over_mean</span><span class="special">,</span> <span class="identifier">standard_deviation</span><span class="special">);</span>
@@ -141,7 +136,6 @@
thus:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">under_fraction</span> <span class="special">=</span> <span class="number">0.05</span><span class="special">;</span> <span class="comment">// so 95% are above the minimum weight mean - sd = 2.9</span>
<span class="keyword">double</span> <span class="identifier">low_limit</span> <span class="special">=</span> <span class="identifier">standard_deviation</span><span class="special">;</span>
@@ -163,7 +157,6 @@
To use this we will need to
</p>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">find_location</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">find_location</span><span class="special">;</span></pre>
@@ -174,7 +167,6 @@
a new normal distribution called 'goodpacks'.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">safe_mean</span> <span class="special">=</span> <span class="identifier">find_location</span><span class="special"><</span><span class="identifier">normal</span><span class="special">>(</span><span class="identifier">minimum_weight</span><span class="special">,</span> <span class="identifier">under_fraction</span><span class="special">,</span> <span class="identifier">standard_deviation</span><span class="special">);</span>
<span class="identifier">normal</span> <span class="identifier">good_packs</span><span class="special">(</span><span class="identifier">safe_mean</span><span class="special">,</span> <span class="identifier">standard_deviation</span><span class="special">);</span></pre>
@@ -184,7 +176,6 @@
with the same confirmation as before:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Setting the packer to "</span> <span class="special"><<</span> <span class="identifier">nominal_mean</span> <span class="special"><<</span> <span class="string">" will mean that "</span>
<span class="special"><<</span> <span class="string">"fraction of packs >= "</span> <span class="special"><<</span> <span class="identifier">minimum_weight</span>
@@ -192,9 +183,9 @@
<span class="comment">// Setting the packer to 3.06449 will mean that fraction of packs >= 2.9 is 0.95</span></pre>
<p>
</p>
-<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.using_cauchy_lorentz_instead_of_normal_distribution"></a><h5>
-<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.using_cauchy_lorentz_instead_of_normal_distribution-heading"></a>
- <a class="link" href="find_mean_and_sd_eg.html#math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.using_cauchy_lorentz_instead_of_normal_distribution">Using
+<h5>
+<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.h1"></a>
+ <span><a name="math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.using_cauchy_lorentz_instead_of_normal_distribution"></a></span><a class="link" href="find_mean_and_sd_eg.html#math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.using_cauchy_lorentz_instead_of_normal_distribution">Using
Cauchy-Lorentz instead of normal distribution</a>
</h5>
<p>
@@ -217,7 +208,6 @@
and estimate the fraction that lie below our minimum weight specification.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cauchy</span> <span class="identifier">cpacks</span><span class="special">(</span><span class="identifier">mean</span><span class="special">,</span> <span class="identifier">standard_deviation</span><span class="special">);</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Cauchy Setting the packer to "</span> <span class="special"><<</span> <span class="identifier">mean</span> <span class="special"><<</span> <span class="string">" will mean that "</span>
@@ -232,7 +222,6 @@
as template parameter, in place of the normal used above.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">lc</span> <span class="special">=</span> <span class="identifier">find_location</span><span class="special"><</span><span class="identifier">cauchy</span><span class="special">>(</span><span class="identifier">minimum_weight</span><span class="special">,</span> <span class="identifier">under_fraction</span><span class="special">,</span> <span class="identifier">standard_deviation</span><span class="special">);</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"find_location<cauchy>(minimum_weight, over fraction, standard_deviation); "</span> <span class="special"><<</span> <span class="identifier">lc</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
@@ -247,7 +236,6 @@
And again confirm that the fraction meeting specification is as expected.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cauchy</span> <span class="identifier">goodcpacks</span><span class="special">(</span><span class="identifier">lc</span><span class="special">,</span> <span class="identifier">standard_deviation</span><span class="special">);</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Cauchy Setting the packer to "</span> <span class="special"><<</span> <span class="identifier">lc</span> <span class="special"><<</span> <span class="string">" will mean that "</span>
@@ -261,7 +249,6 @@
that 99% of packs met the specification.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Cauchy Setting the packer to "</span>
<span class="special"><<</span> <span class="identifier">find_location</span><span class="special"><</span><span class="identifier">cauchy</span><span class="special">>(</span><span class="identifier">minimum_weight</span><span class="special">,</span> <span class="number">0.99</span><span class="special">,</span> <span class="identifier">standard_deviation</span><span class="special">)</span>
@@ -304,9 +291,9 @@
Intervals on the standard deviation</a> for a worked example chi_square_std_dev_test.cpp
of estimating these intervals.
</p>
-<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.changing_the_scale_or_standard_deviation"></a><h5>
-<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.changing_the_scale_or_standard_deviation-heading"></a>
- <a class="link" href="find_mean_and_sd_eg.html#math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.changing_the_scale_or_standard_deviation">Changing
+<h5>
+<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.h2"></a>
+ <span><a name="math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.changing_the_scale_or_standard_deviation"></a></span><a class="link" href="find_mean_and_sd_eg.html#math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.changing_the_scale_or_standard_deviation">Changing
the scale or standard deviation</a>
</h5>
<p>
@@ -323,7 +310,6 @@
under_weight limit, 2.9
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="number">0.05</span><span class="special">;</span> <span class="comment">// wanted p th quantile.</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Quantile of "</span> <span class="special"><<</span> <span class="identifier">p</span> <span class="special"><<</span> <span class="string">" = "</span> <span class="special"><<</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">packs</span><span class="special">,</span> <span class="identifier">p</span><span class="special">)</span>
@@ -343,7 +329,6 @@
standard deviation of 0.05 kg.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">normal</span> <span class="identifier">pack05</span><span class="special">(</span><span class="identifier">mean</span><span class="special">,</span> <span class="number">0.05</span><span class="special">);</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Quantile of "</span> <span class="special"><<</span> <span class="identifier">p</span> <span class="special"><<</span> <span class="string">" = "</span> <span class="special"><<</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">pack05</span><span class="special">,</span> <span class="identifier">p</span><span class="special">)</span>
@@ -363,7 +348,6 @@
to 0.06 kg, constructing another new distribution called pack06.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">normal</span> <span class="identifier">pack06</span><span class="special">(</span><span class="identifier">mean</span><span class="special">,</span> <span class="number">0.06</span><span class="special">);</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Quantile of "</span> <span class="special"><<</span> <span class="identifier">p</span> <span class="special"><<</span> <span class="string">" = "</span> <span class="special"><<</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">pack06</span><span class="special">,</span> <span class="identifier">p</span><span class="special">)</span>
@@ -402,7 +386,6 @@
Rearranging, we can directly calculate the required standard deviation:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">normal</span> <span class="identifier">N01</span><span class="special">;</span> <span class="comment">// standard normal distribution with meamn zero and unit standard deviation.</span>
<span class="identifier">p</span> <span class="special">=</span> <span class="number">0.05</span><span class="special">;</span>
@@ -419,7 +402,6 @@
packer, and check that our distribution will meet the specification.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">normal</span> <span class="identifier">pack95</span><span class="special">(</span><span class="identifier">mean</span><span class="special">,</span> <span class="identifier">sd95</span><span class="special">);</span>
<span class="identifier">cout</span> <span class="special"><<</span><span class="string">"Fraction of packs >= "</span> <span class="special"><<</span> <span class="identifier">minimum_weight</span> <span class="special"><<</span> <span class="string">" with a mean of "</span> <span class="special"><<</span> <span class="identifier">mean</span>
@@ -433,7 +415,6 @@
shown below, giving the same standard deviation.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">ss</span> <span class="special">=</span> <span class="identifier">find_scale</span><span class="special"><</span><span class="identifier">normal</span><span class="special">>(</span><span class="identifier">minimum_weight</span><span class="special">,</span> <span class="identifier">under_fraction</span><span class="special">,</span> <span class="identifier">packs</span><span class="special">.</span><span class="identifier">mean</span><span class="special">());</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"find_scale<normal>(minimum_weight, under_fraction, packs.mean()); "</span> <span class="special"><<</span> <span class="identifier">ss</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
@@ -444,7 +425,6 @@
If we had defined an over_fraction, or percentage that must pass specification
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">over_fraction</span> <span class="special">=</span> <span class="number">0.95</span><span class="special">;</span></pre>
<p>
@@ -467,7 +447,6 @@
not over_fraction, thus:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">ss1o</span> <span class="special">=</span> <span class="identifier">find_scale</span><span class="special"><</span><span class="identifier">normal</span><span class="special">>(</span><span class="identifier">minimum_weight</span><span class="special">,</span> <span class="number">1</span> <span class="special">-</span> <span class="identifier">over_fraction</span><span class="special">,</span> <span class="identifier">packs</span><span class="special">.</span><span class="identifier">mean</span><span class="special">());</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"find_scale<normal>(minimum_weight, under_fraction, packs.mean()); "</span> <span class="special"><<</span> <span class="identifier">ss1o</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
@@ -481,7 +460,6 @@
giving the most accurate result.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">ssc</span> <span class="special">=</span> <span class="identifier">find_scale</span><span class="special"><</span><span class="identifier">normal</span><span class="special">>(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">minimum_weight</span><span class="special">,</span> <span class="identifier">over_fraction</span><span class="special">,</span> <span class="identifier">packs</span><span class="special">.</span><span class="identifier">mean</span><span class="special">()));</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"find_scale<normal>(complement(minimum_weight, over_fraction, packs.mean())); "</span> <span class="special"><<</span> <span class="identifier">ssc</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
@@ -495,7 +473,6 @@
We can again confirm our prediction thus:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">normal</span> <span class="identifier">pack95c</span><span class="special">(</span><span class="identifier">mean</span><span class="special">,</span> <span class="identifier">ssc</span><span class="special">);</span>
<span class="identifier">cout</span> <span class="special"><<</span><span class="string">"Fraction of packs >= "</span> <span class="special"><<</span> <span class="identifier">minimum_weight</span> <span class="special"><<</span> <span class="string">" with a mean of "</span> <span class="special"><<</span> <span class="identifier">mean</span>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -33,12 +33,11 @@
of course).
</p>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> <span class="comment">// for normal_distribution</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">normal</span><span class="special">;</span> <span class="comment">// typedef provides default type is double.</span>
<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">find_scale</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
- <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">find_scale</span><span class="special">;</span>
+ <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">find_scale</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">complement</span><span class="special">;</span> <span class="comment">// Needed if you want to use the complement version.</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">;</span> <span class="comment">// Needed to specify the error handling policy.</span>
@@ -58,7 +57,6 @@
constructor.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">normal</span> <span class="identifier">N01</span><span class="special">;</span> <span class="comment">// Default 'standard' normal distribution with zero mean</span>
<span class="keyword">double</span> <span class="identifier">sd</span> <span class="special">=</span> <span class="number">1.</span><span class="special">;</span> <span class="comment">// and standard deviation is 1.</span></pre>
@@ -70,14 +68,13 @@
certain chosen limit (here -2. standard deviations).
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">z</span> <span class="special">=</span> <span class="special">-</span><span class="number">2.</span><span class="special">;</span> <span class="comment">// z to give prob p</span>
<span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="number">0.001</span><span class="special">;</span> <span class="comment">// only 0.1% below z = -2</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Normal distribution with mean = "</span> <span class="special"><<</span> <span class="identifier">N01</span><span class="special">.</span><span class="identifier">location</span><span class="special">()</span> <span class="comment">// aka N01.mean()</span>
<span class="special"><<</span> <span class="string">", standard deviation "</span> <span class="special"><<</span> <span class="identifier">N01</span><span class="special">.</span><span class="identifier">scale</span><span class="special">()</span> <span class="comment">// aka N01.standard_deviation()</span>
- <span class="special"><<</span> <span class="string">", has "</span> <span class="special"><<</span> <span class="string">"fraction <= "</span> <span class="special"><<</span> <span class="identifier">z</span>
+ <span class="special"><<</span> <span class="string">", has "</span> <span class="special"><<</span> <span class="string">"fraction <= "</span> <span class="special"><<</span> <span class="identifier">z</span>
<span class="special"><<</span> <span class="string">", p = "</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">N01</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Normal distribution with mean = "</span> <span class="special"><<</span> <span class="identifier">N01</span><span class="special">.</span><span class="identifier">location</span><span class="special">()</span>
<span class="special"><<</span> <span class="string">", standard deviation "</span> <span class="special"><<</span> <span class="identifier">N01</span><span class="special">.</span><span class="identifier">scale</span><span class="special">()</span>
@@ -94,7 +91,6 @@
a new standard deviation.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">l</span> <span class="special">=</span> <span class="identifier">N01</span><span class="special">.</span><span class="identifier">location</span><span class="special">();</span>
<span class="keyword">double</span> <span class="identifier">s</span> <span class="special">=</span> <span class="identifier">find_scale</span><span class="special"><</span><span class="identifier">normal</span><span class="special">>(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">l</span><span class="special">);</span>
@@ -114,7 +110,6 @@
a new distribution with the new standard deviation (but same zero mean):
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">normal</span> <span class="identifier">np001pc</span><span class="special">(</span><span class="identifier">N01</span><span class="special">.</span><span class="identifier">location</span><span class="special">(),</span> <span class="identifier">s</span><span class="special">);</span></pre>
<p>
@@ -123,22 +118,21 @@
And re-calculating the fraction below (and above) our chosen limit.
</p>
<p>
-
</p>
-<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Normal distribution with mean = "</span> <span class="special"><<</span> <span class="identifier">l</span>
- <span class="special"><<</span> <span class="string">" has "</span> <span class="special"><<</span> <span class="string">"fraction <= "</span> <span class="special"><<</span> <span class="identifier">z</span>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Normal distribution with mean = "</span> <span class="special"><<</span> <span class="identifier">l</span>
+ <span class="special"><<</span> <span class="string">" has "</span> <span class="special"><<</span> <span class="string">"fraction <= "</span> <span class="special"><<</span> <span class="identifier">z</span>
<span class="special"><<</span> <span class="string">", p = "</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">np001pc</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
-<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Normal distribution with mean = "</span> <span class="special"><<</span> <span class="identifier">l</span>
- <span class="special"><<</span> <span class="string">" has "</span> <span class="special"><<</span> <span class="string">"fraction > "</span> <span class="special"><<</span> <span class="identifier">z</span>
+<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Normal distribution with mean = "</span> <span class="special"><<</span> <span class="identifier">l</span>
+ <span class="special"><<</span> <span class="string">" has "</span> <span class="special"><<</span> <span class="string">"fraction > "</span> <span class="special"><<</span> <span class="identifier">z</span>
<span class="special"><<</span> <span class="string">", p = "</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">np001pc</span><span class="special">,</span> <span class="identifier">z</span><span class="special">))</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span></pre>
<p>
</p>
<pre class="programlisting">Normal distribution with mean = 0 has fraction <= -2, p = 0.001
Normal distribution with mean = 0 has fraction > -2, p = 0.999
</pre>
-<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_scale_eg.controlling_how_errors_from_find_scale_are_handled"></a><h5>
-<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_scale_eg.controlling_how_errors_from_find_scale_are_handled-heading"></a>
- <a class="link" href="find_scale_eg.html#math_toolkit.dist.stat_tut.weg.find_eg.find_scale_eg.controlling_how_errors_from_find_scale_are_handled">Controlling
+<h5>
+<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_scale_eg.h0"></a>
+ <span><a name="math_toolkit.dist.stat_tut.weg.find_eg.find_scale_eg.controlling_how_errors_from_find_scale_are_handled"></a></span><a class="link" href="find_scale_eg.html#math_toolkit.dist.stat_tut.weg.find_eg.find_scale_eg.controlling_how_errors_from_find_scale_are_handled">Controlling
how Errors from find_scale are handled</a>
</h5>
<p>
@@ -150,7 +144,6 @@
Unless we are using the boost::math namespace, we will need:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">domain_error</span><span class="special">;</span>
@@ -162,7 +155,6 @@
it is not required, as the various examples below show.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special"><</span><span class="identifier">domain_error</span><span class="special"><</span><span class="identifier">ignore_error</span><span class="special">></span> <span class="special">></span> <span class="identifier">ignore_domain_policy</span><span class="special">;</span>
<span class="comment">// find_scale with new policy, using typedef.</span>
@@ -184,16 +176,15 @@
use the <a class="link" href="../../overview/complements.html#complements">complements</a> version.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">z</span> <span class="special">=</span> <span class="special">-</span><span class="number">2.</span><span class="special">;</span>
<span class="keyword">double</span> <span class="identifier">q</span> <span class="special">=</span> <span class="number">0.999</span><span class="special">;</span> <span class="comment">// = 1 - p; // complement of 0.001.</span>
<span class="identifier">sd</span> <span class="special">=</span> <span class="identifier">find_scale</span><span class="special"><</span><span class="identifier">normal</span><span class="special">>(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">q</span><span class="special">,</span> <span class="identifier">l</span><span class="special">));</span>
<span class="identifier">normal</span> <span class="identifier">np95pc</span><span class="special">(</span><span class="identifier">l</span><span class="special">,</span> <span class="identifier">sd</span><span class="special">);</span> <span class="comment">// Same standard_deviation (scale) but with mean(scale) shifted</span>
-<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Normal distribution with mean = "</span> <span class="special"><<</span> <span class="identifier">l</span> <span class="special"><<</span> <span class="string">" has "</span>
+<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Normal distribution with mean = "</span> <span class="special"><<</span> <span class="identifier">l</span> <span class="special"><<</span> <span class="string">" has "</span>
<span class="special"><<</span> <span class="string">"fraction <= "</span> <span class="special"><<</span> <span class="identifier">z</span> <span class="special"><<</span> <span class="string">" = "</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">np95pc</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
-<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Normal distribution with mean = "</span> <span class="special"><<</span> <span class="identifier">l</span> <span class="special"><<</span> <span class="string">" has "</span>
+<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Normal distribution with mean = "</span> <span class="special"><<</span> <span class="identifier">l</span> <span class="special"><<</span> <span class="string">" has "</span>
<span class="special"><<</span> <span class="string">"fraction > "</span> <span class="special"><<</span> <span class="identifier">z</span> <span class="special"><<</span> <span class="string">" = "</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">np95pc</span><span class="special">,</span> <span class="identifier">z</span><span class="special">))</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span></pre>
<p>
</p>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/geometric_eg.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/geometric_eg.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/geometric_eg.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -35,7 +35,6 @@
a discrete_quantile policy of real, rather than the default policy integer_round_outwards.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_OVERFLOW_ERROR_POLICY</span> <span class="identifier">ignore_error</span>
<span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_DISCRETE_QUANTILE_POLICY</span> <span class="identifier">real</span></pre>
@@ -56,7 +55,6 @@
binomial distribution, and we need some std library iostream, of course.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">geometric</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
<span class="comment">// for geometric_distribution</span>
@@ -78,7 +76,7 @@
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">noshowpoint</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">fixed</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">left</span><span class="special">;</span>
<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iomanip</span><span class="special">></span>
- <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">;</span>
+ <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">;</span>
<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">limits</span><span class="special">></span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">;</span>
@@ -93,9 +91,9 @@
Simple try'n'catch blocks (see below) will ensure that you get a helpful
error message instead of an abrupt (and silent) program abort.
</p>
-<a name="math_toolkit.dist.stat_tut.weg.geometric_eg.throwing_a_dice"></a><h6>
-<a name="math_toolkit.dist.stat_tut.weg.geometric_eg.throwing_a_dice-heading"></a>
- <a class="link" href="geometric_eg.html#math_toolkit.dist.stat_tut.weg.geometric_eg.throwing_a_dice">Throwing
+<h6>
+<a name="math_toolkit.dist.stat_tut.weg.geometric_eg.h0"></a>
+ <span><a name="math_toolkit.dist.stat_tut.weg.geometric_eg.throwing_a_dice"></a></span><a class="link" href="geometric_eg.html#math_toolkit.dist.stat_tut.weg.geometric_eg.throwing_a_dice">Throwing
a dice</a>
</h6>
<p>
@@ -109,7 +107,6 @@
Suppose an 'fair' 6-face dice is thrown repeatedly:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">success_fraction</span> <span class="special">=</span> <span class="number">1.</span><span class="special">/</span><span class="number">6</span><span class="special">;</span> <span class="comment">// success_fraction (p) = 0.1666</span>
<span class="comment">// (so failure_fraction is 1 - success_fraction = 5./6 = 1- 0.1666 = 0.8333)</span></pre>
@@ -128,7 +125,6 @@
one parameter success_fraction, the probability of success.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">geometric</span> <span class="identifier">g6</span><span class="special">(</span><span class="identifier">success_fraction</span><span class="special">);</span> <span class="comment">// type double by default.</span></pre>
<p>
@@ -137,7 +133,6 @@
To confirm, we can echo the success_fraction parameter of the distribution.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"success fraction of a six-sided dice is "</span> <span class="special"><<</span> <span class="identifier">g6</span><span class="special">.</span><span class="identifier">success_fraction</span><span class="special">()</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span></pre>
<p>
@@ -147,7 +142,6 @@
is
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">g6</span><span class="special">,</span> <span class="number">0</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.1667</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">g6</span><span class="special">,</span> <span class="number">0</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.1667</span></pre>
@@ -159,7 +153,6 @@
on the 2nd throw:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">g6</span><span class="special">,</span> <span class="number">1</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.1389</span></pre>
<p>
@@ -169,7 +162,6 @@
on the 1st or 2nd throw (allowing one failure):
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"pdf(g6, 0) + pdf(g6, 1) = "</span> <span class="special"><<</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">g6</span><span class="special">,</span> <span class="number">0</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">g6</span><span class="special">,</span> <span class="number">1</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span></pre>
<p>
@@ -179,7 +171,6 @@
Function CDF.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"cdf(g6, 1) = "</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">g6</span><span class="special">,</span> <span class="number">1</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.3056</span></pre>
<p>
@@ -189,7 +180,6 @@
gets very high:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"cdf(g6, 12) = "</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">g6</span><span class="special">,</span> <span class="number">12</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.9065 or 90% probability.</span></pre>
<p>
@@ -199,7 +189,6 @@
of throws to be this sure using the inverse or quantile.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"quantile(g6, 0.99) = "</span> <span class="special"><<</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">g6</span><span class="special">,</span> <span class="number">0.99</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 24.26</span></pre>
<p>
@@ -218,7 +207,6 @@
be faster, and may be more accurate.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">negative_binomial</span> <span class="identifier">nb</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="identifier">success_fraction</span><span class="special">);</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">1</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.1389</span>
@@ -230,7 +218,6 @@
- 0.99 = 0.01 (and get the same result):
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"quantile(complement(g6, 1 - p)) "</span> <span class="special"><<</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">g6</span><span class="special">,</span> <span class="number">0.01</span><span class="special">))</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 24.26</span></pre>
<p>
@@ -250,19 +237,18 @@
So in Boost.Math the equivalent is
</p>
<p>
-
</p>
<pre class="programlisting"> <span class="identifier">geometric</span> <span class="identifier">g05</span><span class="special">(</span><span class="number">0.5</span><span class="special">);</span> <span class="comment">// Probability of success = 0.5 or 50%</span>
<span class="comment">// Output all potentially significant digits for the type, here double.</span>
<span class="preprocessor">#ifdef</span> <span class="identifier">BOOST_NO_NUMERIC_LIMITS_LOWEST</span>
<span class="keyword">int</span> <span class="identifier">max_digits10</span> <span class="special">=</span> <span class="number">2</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">digits</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special"><></span> <span class="special">>()</span> <span class="special">*</span> <span class="number">30103UL</span><span class="special">)</span> <span class="special">/</span> <span class="number">100000UL</
span><span class="special">;</span>
- <span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"BOOST_NO_NUMERIC_LIMITS_LOWEST is defined"</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
-<span class="preprocessor">#else</span>
+ <span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"BOOST_NO_NUMERIC_LIMITS_LOWEST is defined"</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="preprocessor">#else</span>
<span class="keyword">int</span> <span class="identifier">max_digits10</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">;</span>
<span class="preprocessor">#endif</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Show all potentially significant decimal digits std::numeric_limits<double>::max_digits10 = "</span>
- <span class="special"><<</span> <span class="identifier">max_digits10</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
+ <span class="special"><<</span> <span class="identifier">max_digits10</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">max_digits10</span><span class="special">);</span> <span class="comment">// </span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">g05</span><span class="special">,</span> <span class="number">0.0001</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// returns 0.5000346561579232, not exact 0.5.</span></pre>
@@ -273,7 +259,6 @@
the <code class="computeroutput"><span class="identifier">floor</span></code> function.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">g05</span><span class="special">,</span> <span class="identifier">floor</span><span class="special">(</span><span class="number">0.0001</span><span class="special">))</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// returns exactly 0.5</span></pre>
<p>
@@ -287,9 +272,9 @@
next integer above. This may be convenient in practice, and could be
replicated in C++ if desired.
</p>
-<a name="math_toolkit.dist.stat_tut.weg.geometric_eg.surveying_customers_to_find_one_with_a_faulty_product"></a><h6>
-<a name="math_toolkit.dist.stat_tut.weg.geometric_eg.surveying_customers_to_find_one_with_a_faulty_product-heading"></a>
- <a class="link" href="geometric_eg.html#math_toolkit.dist.stat_tut.weg.geometric_eg.surveying_customers_to_find_one_with_a_faulty_product">Surveying
+<h6>
+<a name="math_toolkit.dist.stat_tut.weg.geometric_eg.h1"></a>
+ <span><a name="math_toolkit.dist.stat_tut.weg.geometric_eg.surveying_customers_to_find_one_with_a_faulty_product"></a></span><a class="link" href="geometric_eg.html#math_toolkit.dist.stat_tut.weg.geometric_eg.surveying_customers_to_find_one_with_a_faulty_product">Surveying
customers to find one with a faulty product</a>
</h6>
<p>
@@ -312,29 +297,28 @@
a fault obviously improves.)
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="number">5</span><span class="special">);</span>
<span class="identifier">geometric</span> <span class="identifier">g</span><span class="special">(</span><span class="number">0.02</span><span class="special">);</span> <span class="comment">// On average, 2 in 100 products are faulty.</span>
<span class="keyword">double</span> <span class="identifier">c</span> <span class="special">=</span> <span class="number">0.95</span><span class="special">;</span> <span class="comment">// 95% confidence.</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">" quantile(g, "</span> <span class="special"><<</span> <span class="identifier">c</span> <span class="special"><<</span> <span class="string">") = "</span> <span class="special"><<</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">g</span><span class="special">,</span> <span class="identifier">c</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
-<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"To be "</span> <span class="special"><<</span> <span class="identifier">c</span> <span class="special">*</span> <span class="number">100</span>
+<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"To be "</span> <span class="special"><<</span> <span class="identifier">c</span> <span class="special">*</span> <span class="number">100</span>
<span class="special"><<</span> <span class="string">"% confident of finding we customer with a fault, need to survey "</span>
<span class="special"><<</span> <span class="identifier">ceil</span><span class="special">(</span><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">g</span><span class="special">,</span> <span class="identifier">c</span><span class="special">))</span> <span class="special"><<</span> <span class="string">" customers."</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 148</span>
<span class="identifier">c</span> <span class="special">=</span> <span class="number">0.99</span><span class="special">;</span> <span class="comment">// Very confident.</span>
-<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"To be "</span> <span class="special"><<</span> <span class="identifier">c</span> <span class="special">*</span> <span class="number">100</span>
+<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"To be "</span> <span class="special"><<</span> <span class="identifier">c</span> <span class="special">*</span> <span class="number">100</span>
<span class="special"><<</span> <span class="string">"% confident of finding we customer with a fault, need to survey "</span>
<span class="special"><<</span> <span class="identifier">ceil</span><span class="special">(</span><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">g</span><span class="special">,</span> <span class="identifier">c</span><span class="special">))</span> <span class="special"><<</span> <span class="string">" customers."</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 227</span>
<span class="identifier">c</span> <span class="special">=</span> <span class="number">0.80</span><span class="special">;</span> <span class="comment">// Only reasonably confident.</span>
-<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"To be "</span> <span class="special"><<</span> <span class="identifier">c</span> <span class="special">*</span> <span class="number">100</span>
+<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"To be "</span> <span class="special"><<</span> <span class="identifier">c</span> <span class="special">*</span> <span class="number">100</span>
<span class="special"><<</span> <span class="string">"% confident of finding we customer with a fault, need to survey "</span>
<span class="special"><<</span> <span class="identifier">ceil</span><span class="special">(</span><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">g</span><span class="special">,</span> <span class="identifier">c</span><span class="special">))</span> <span class="special"><<</span> <span class="string">" customers."</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 79</span></pre>
<p>
</p>
-<a name="math_toolkit.dist.stat_tut.weg.geometric_eg.basket_ball_shooters"></a><h6>
-<a name="math_toolkit.dist.stat_tut.weg.geometric_eg.basket_ball_shooters-heading"></a>
- <a class="link" href="geometric_eg.html#math_toolkit.dist.stat_tut.weg.geometric_eg.basket_ball_shooters">Basket
+<h6>
+<a name="math_toolkit.dist.stat_tut.weg.geometric_eg.h2"></a>
+ <span><a name="math_toolkit.dist.stat_tut.weg.geometric_eg.basket_ball_shooters"></a></span><a class="link" href="geometric_eg.html#math_toolkit.dist.stat_tut.weg.geometric_eg.basket_ball_shooters">Basket
Ball Shooters</a>
</h6>
<p>
@@ -346,7 +330,6 @@
a geometric distribution with success_fraction parameter 75/100 = 0.75.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="number">2</span><span class="special">);</span>
<span class="identifier">geometric</span> <span class="identifier">gav</span><span class="special">(</span><span class="number">0.75</span><span class="special">);</span> <span class="comment">// Shooter averages 7.5 out of 10 in the basket.</span></pre>
@@ -357,7 +340,6 @@
failures?
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of score on 1st try = "</span> <span class="special"><<</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">gav</span><span class="special">,</span> <span class="number">0</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.75</span></pre>
<p>
@@ -368,7 +350,6 @@
are 5-1 = 4 failures before the first success.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of score on 5th try = "</span> <span class="special"><<</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">gav</span><span class="special">,</span> <span class="number">4</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.0029</span></pre>
<p>
@@ -380,7 +361,6 @@
values:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">geometric</span> <span class="identifier">gbest</span><span class="special">(</span><span class="number">0.95</span><span class="special">);</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of score on 5th try = "</span> <span class="special"><<</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">gbest</span><span class="special">,</span> <span class="number">4</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 5.9e-6</span>
@@ -392,9 +372,9 @@
So we can see the very much smaller chance (0.000006) of 4 failures by
the best shooters, compared to the 0.03 of the mediocre.
</p>
-<a name="math_toolkit.dist.stat_tut.weg.geometric_eg.estimating_failures"></a><h6>
-<a name="math_toolkit.dist.stat_tut.weg.geometric_eg.estimating_failures-heading"></a>
- <a class="link" href="geometric_eg.html#math_toolkit.dist.stat_tut.weg.geometric_eg.estimating_failures">Estimating
+<h6>
+<a name="math_toolkit.dist.stat_tut.weg.geometric_eg.h3"></a>
+ <span><a name="math_toolkit.dist.stat_tut.weg.geometric_eg.estimating_failures"></a></span><a class="link" href="geometric_eg.html#math_toolkit.dist.stat_tut.weg.geometric_eg.estimating_failures">Estimating
failures</a>
</h6>
<p>
@@ -419,13 +399,12 @@
must divide alpha by two.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">alpha</span> <span class="special">=</span> <span class="number">0.05</span><span class="special">;</span>
<span class="keyword">double</span> <span class="identifier">k</span> <span class="special">=</span> <span class="number">100</span><span class="special">;</span> <span class="comment">// So frequency of occurence is 1/100.</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability is failure is "</span> <span class="special"><<</span> <span class="number">1</span><span class="special">/</span><span class="identifier">k</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">double</span> <span class="identifier">t</span> <span class="special">=</span> <span class="identifier">geometric</span><span class="special">::</span><span class="identifier">find_lower_bound_on_p</span><span class="special">(</span><span class="identifier">k</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">/</span><span class="number">2</span><span class="special">);</span>
-<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"geometric::find_lower_bound_on_p("</span> <span class="special"><<</span> <span class="keyword">int</span><span class="special">(</span><span class="identifier">k</span><span class="special">)</span> <span class="special"><<</span> <span class="string">", "</span> <span class="special"><<</span> <span class="identifier">alpha</span><span class="special">/</span><span class="number">2</span> <span class="special"><<</span> <span class="string">") = "</span>
+<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"geometric::find_lower_bound_on_p("</span> <span class="special"><<</span> <span class="keyword">int</span><span class="special">(</span><span class="identifier">k</span><span class="special">)</span> <span class="special"><<</span> <span class="string">", "</span> <span class="special"><<</span> <span class="identifier">alpha</span><span class="special">/</span><span class="number">2</span> <span class="special"><<</span> <span class="string">") = "</span>
<span class="special"><<</span> <span class="identifier">t</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.00025</span>
<span class="identifier">t</span> <span class="special">=</span> <span class="identifier">geometric</span><span class="special">::</span><span class="identifier">find_upper_bound_on_p</span><span class="special">(</span><span class="identifier">k</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">/</span><span class="number">2</span><span class="special">);</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"geometric::find_upper_bound_on_p("</span> <span class="special"><<</span> <span class="keyword">int</span><span class="special">(</span><span class="identifier">k</span><span class="special">)</span> <span class="special"><<</span> <span class="string">", "</span> <span class="special"><<</span> <span class="identifier">alpha</span><span class="special">/</span><span class="number">2</span> <span class="special"><<</span> <span class="string">") = "</span>
@@ -439,7 +418,6 @@
they widen to 0.00005 to 0.05.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">alpha</span> <span class="special">=</span> <span class="number">0.1</span><span class="special">;</span> <span class="comment">// 90% confidence.</span>
<span class="identifier">t</span> <span class="special">=</span> <span class="identifier">geometric</span><span class="special">::</span><span class="identifier">find_lower_bound_on_p</span><span class="special">(</span><span class="identifier">k</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">/</span><span class="number">2</span><span class="special">);</span>
@@ -468,7 +446,6 @@
hope not to use it!
</p>
<p>
-
</p>
<pre class="programlisting"><span class="special">}</span>
<span class="keyword">catch</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exception</span><span class="special">&</span> <span class="identifier">e</span><span class="special">)</span>
@@ -478,7 +455,7 @@
<p>
</p>
<p>
- For example, without a ignore domain error policy, if we asked for
+ For example, without a ignore domain error policy, if we asked for
</p>
<pre class="programlisting"><span class="identifier">pdf</span><span class="special">(</span><span class="identifier">g</span><span class="special">,</span> <span class="special">-</span><span class="number">1</span><span class="special">)</span></pre>
<p>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/inverse_chi_squared_eg.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/inverse_chi_squared_eg.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/inverse_chi_squared_eg.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -95,9 +95,9 @@
in a Bayesian analysis with data on a specific single machine to derive
a posterior distribution for that machine.
</p>
-<a name="math_toolkit.dist.stat_tut.weg.inverse_chi_squared_eg.step_one__using_the_survey_information_"></a><h6>
-<a name="math_toolkit.dist.stat_tut.weg.inverse_chi_squared_eg.step_one__using_the_survey_information_-heading"></a>
- <a class="link" href="inverse_chi_squared_eg.html#math_toolkit.dist.stat_tut.weg.inverse_chi_squared_eg.step_one__using_the_survey_information_">Step
+<h6>
+<a name="math_toolkit.dist.stat_tut.weg.inverse_chi_squared_eg.h0"></a>
+ <span><a name="math_toolkit.dist.stat_tut.weg.inverse_chi_squared_eg.step_one__using_the_survey_information_"></a></span><a class="link" href="inverse_chi_squared_eg.html#math_toolkit.dist.stat_tut.weg.inverse_chi_squared_eg.step_one__using_the_survey_information_">Step
one: Using the survey information.</a>
</h6>
<p>
@@ -118,10 +118,9 @@
list out a few quantiles:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">priorDF</span> <span class="special">=</span> <span class="number">20.0</span><span class="special">;</span>
-<span class="keyword">double</span> <span class="identifier">priorScale</span> <span class="special">=</span> <span class="number">25.0</span><span class="special">;</span>
+<span class="keyword">double</span> <span class="identifier">priorScale</span> <span class="special">=</span> <span class="number">25.0</span><span class="special">;</span>
<span class="identifier">inverse_chi_squared</span> <span class="identifier">prior</span><span class="special">(</span><span class="identifier">priorDF</span><span class="special">,</span> <span class="identifier">priorScale</span><span class="special">);</span>
<span class="comment">// Using an inverse_gamma distribution instead, we could equivalently write</span>
@@ -152,11 +151,10 @@
and find a probability of about 0.031 (3.1%) for each case.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">" probability variance <= 15: "</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">prior</span><span class="special">,</span> <span class="number">15.0</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">" probability variance <= 25: "</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">prior</span><span class="special">,</span> <span class="number">25.0</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
-<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">" probability variance > 50: "</span>
+<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">" probability variance > 50: "</span>
<span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">prior</span><span class="special">,</span> <span class="number">50.0</span><span class="special">))</span>
<span class="special"><<</span> <span class="identifier">endl</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
</pre>
@@ -185,9 +183,9 @@
interpretationally a strict <span class="emphasis"><em>must-not</em></span>) in the frequentist
world.
</p>
-<a name="math_toolkit.dist.stat_tut.weg.inverse_chi_squared_eg.step_2__investigate_a_single_machine"></a><h6>
-<a name="math_toolkit.dist.stat_tut.weg.inverse_chi_squared_eg.step_2__investigate_a_single_machine-heading"></a>
- <a class="link" href="inverse_chi_squared_eg.html#math_toolkit.dist.stat_tut.weg.inverse_chi_squared_eg.step_2__investigate_a_single_machine">Step
+<h6>
+<a name="math_toolkit.dist.stat_tut.weg.inverse_chi_squared_eg.h1"></a>
+ <span><a name="math_toolkit.dist.stat_tut.weg.inverse_chi_squared_eg.step_2__investigate_a_single_machine"></a></span><a class="link" href="inverse_chi_squared_eg.html#math_toolkit.dist.stat_tut.weg.inverse_chi_squared_eg.step_2__investigate_a_single_machine">Step
2: Investigate a single machine</a>
</h6>
<p>
@@ -233,7 +231,6 @@
with degrees-of-freedom (ν<sub>posterior</sub>) = 120 and scale (s<sub>posterior</sub>) = 49.54.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">ballsSampleSize</span> <span class="special">=</span> <span class="number">100</span><span class="special">;</span>
<span class="identifier">cout</span> <span class="special"><<</span><span class="string">"balls sample size: "</span> <span class="special"><<</span> <span class="identifier">ballsSampleSize</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
@@ -244,7 +241,7 @@
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"prior degrees-of-freedom: "</span> <span class="special"><<</span> <span class="identifier">priorDF</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"posterior degrees-of-freedom: "</span> <span class="special"><<</span> <span class="identifier">posteriorDF</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
-<span class="keyword">double</span> <span class="identifier">posteriorScale</span> <span class="special">=</span>
+<span class="keyword">double</span> <span class="identifier">posteriorScale</span> <span class="special">=</span>
<span class="special">(</span><span class="identifier">priorDF</span> <span class="special">*</span> <span class="identifier">priorScale</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">ballsSampleVariance</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">ballsSampleSize</span> <span class="special">-</span> <span class="number">1</span><span class="special">)))</span> <span class="special">/</span> <span class="identifier">posteriorDF</span><span class="special">;</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"prior scale: "</span> <span class="special"><<</span> <span class="identifier">priorScale</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"posterior scale: "</span> <span class="special"><<</span> <span class="identifier">posteriorScale</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span></pre>
@@ -275,7 +272,6 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/prior_posterior_plot.png" align="middle"></span>
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">inverse_chi_squared</span> <span class="identifier">posterior</span><span class="special">(</span><span class="identifier">posteriorDF</span><span class="special">,</span> <span class="identifier">posteriorScale</span><span class="special">);</span>
@@ -286,7 +282,7 @@
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">" probability variance <= 15: "</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">posterior</span><span class="special">,</span> <span class="number">15.0</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">" probability variance <= 25: "</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">posterior</span><span class="special">,</span> <span class="number">25.0</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
- <span class="identifier">cout</span> <span class="special"><<</span> <span class="string">" probability variance > 50: "</span>
+ <span class="identifier">cout</span> <span class="special"><<</span> <span class="string">" probability variance > 50: "</span>
<span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">posterior</span><span class="special">,</span> <span class="number">50.0</span><span class="special">))</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
</pre>
@@ -296,11 +292,11 @@
This produces this output:
</p>
<pre class="programlisting"><span class="identifier">Posterior</span> <span class="identifier">distribution</span><span class="special">:</span>
-
+
<span class="number">2.5</span><span class="special">%</span> <span class="identifier">quantile</span><span class="special">:</span> <span class="number">39.1</span>
<span class="number">50</span><span class="special">%</span> <span class="identifier">quantile</span><span class="special">:</span> <span class="number">49.8</span>
<span class="number">97.5</span><span class="special">%</span> <span class="identifier">quantile</span><span class="special">:</span> <span class="number">64.9</span>
-
+
<span class="identifier">probability</span> <span class="identifier">variance</span> <span class="special"><=</span> <span class="number">15</span><span class="special">:</span> <span class="number">2.97e-031</span>
<span class="identifier">probability</span> <span class="identifier">variance</span> <span class="special"><=</span> <span class="number">25</span><span class="special">:</span> <span class="number">8.85e-010</span>
<span class="identifier">probability</span> <span class="identifier">variance</span> <span class="special">></span> <span class="number">50</span><span class="special">:</span> <span class="number">0.489</span>
@@ -325,18 +321,18 @@
<p>
A full sample output is:
</p>
-<pre class="programlisting">Inverse_chi_squared_distribution Bayes example:
-
+<pre class="programlisting">Inverse_chi_squared_distribution Bayes example:
+
Prior distribution:
-
+
2.5% quantile: 14.6
50% quantile: 25.9
97.5% quantile: 52.1
-
+
probability variance <= 15: 0.031
probability variance <= 25: 0.458
probability variance > 50: 0.0318
-
+
balls sample size: 100
balls sample variance: 55
prior degrees-of-freedom: 20
@@ -344,11 +340,11 @@
prior scale: 25
posterior scale: 49.5
Posterior distribution:
-
+
2.5% quantile: 39.1
50% quantile: 49.8
97.5% quantile: 64.9
-
+
probability variance <= 15: 2.97e-031
probability variance <= 25: 8.85e-010
probability variance > 50: 0.489
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -40,7 +40,6 @@
(and some basic std output of course).
</p>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">non_central_chi_squared</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">chi_squared</span><span class="special">;</span>
@@ -59,7 +58,6 @@
start with a table header:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"[table\n[[[nu]]"</span><span class="special">;</span>
<span class="keyword">for</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">lam</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> <span class="identifier">lam</span> <span class="special"><=</span> <span class="number">20</span><span class="special">;</span> <span class="identifier">lam</span> <span class="special">+=</span> <span class="number">2</span><span class="special">)</span>
@@ -77,7 +75,6 @@
each table cell:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">for</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> <span class="identifier">n</span> <span class="special"><=</span> <span class="number">20</span><span class="special">;</span> <span class="special">++</span><span class="identifier">n</span><span class="special">)</span>
<span class="special">{</span>
@@ -90,7 +87,6 @@
Calculate the χ<sup>2</sup> statistic for a 5% significance:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">cs</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">chi_squared</span><span class="special">(</span><span class="identifier">n</span><span class="special">),</span> <span class="number">0.05</span><span class="special">));</span></pre>
<p>
@@ -100,7 +96,6 @@
non-central χ<sup>2</sup> distribution:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">beta</span> <span class="special">=</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">non_central_chi_squared</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span> <span class="identifier">lam</span><span class="special">),</span> <span class="identifier">cs</span><span class="special">));</span></pre>
<p>
@@ -109,7 +104,6 @@
Then output the cell value:
</p>
<p>
-
</p>
<pre class="programlisting"> <span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"["</span> <span class="special"><<</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">beta</span> <span class="special"><<</span> <span class="string">"]"</span><span class="special">;</span>
<span class="special">}</span>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -59,7 +59,6 @@
(and some basic std output of course).
</p>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">negative_binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">negative_binomial</span><span class="special">;</span>
@@ -76,7 +75,6 @@
that the true occurrence frequency lies outside the calculated interval:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">alpha</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">0.5</span><span class="special">,</span> <span class="number">0.25</span><span class="special">,</span> <span class="number">0.1</span><span class="special">,</span> <span class="number">0.05</span><span class="special">,</span> <span class="number">0.01</span><span class="special">,</span> <span class="number">0.001</span><span class="special">,</span> <span class="number">0.0001</span><span class="special">,</span> <span class="number">0.00001</span> <span class="special">};</span></pre>
<p>
@@ -91,7 +89,6 @@
observed frequency of occurrence that follows a negative binomial distribution.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">void</span> <span class="identifier">confidence_limits_on_frequency</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">trials</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">successes</span><span class="special">)</span>
<span class="special">{</span>
@@ -131,7 +128,6 @@
two.
</p>
<p>
-
</p>
<pre class="programlisting"> <span class="comment">// Now print out the upper and lower limits for the alpha table values.</span>
<span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">)/</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">[</span><span class="number">0</span><span class="special">]);</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span>
@@ -154,7 +150,6 @@
of trials, but always the same success fraction 0.1, or 1 in 10.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
<span class="special">{</span>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -47,7 +47,6 @@
sizes (number of trials) for various probability thresholds:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">void</span> <span class="identifier">find_number_of_trials</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">failures</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">p</span><span class="special">);</span></pre>
<p>
@@ -58,7 +57,6 @@
will be observed.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">alpha</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">0.5</span><span class="special">,</span> <span class="number">0.25</span><span class="special">,</span> <span class="number">0.1</span><span class="special">,</span> <span class="number">0.05</span><span class="special">,</span> <span class="number">0.01</span><span class="special">,</span> <span class="number">0.001</span><span class="special">,</span> <span class="number">0.0001</span><span class="special">,</span> <span class="number">0.00001</span> <span class="special">};</span></pre>
<p>
@@ -81,9 +79,8 @@
rounds this up to ensure we have an integral minimum number of trials.
</p>
<p>
-
</p>
-<pre class="programlisting">
+<pre class="programlisting">
<span class="keyword">void</span> <span class="identifier">find_number_of_trials</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">failures</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">p</span><span class="special">)</span>
<span class="special">{</span>
<span class="comment">// trials = number of trials</span>
@@ -118,7 +115,6 @@
confidence levels:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
<span class="special">{</span>
@@ -148,7 +144,7 @@
number of trials permitted to observe less than a certain number
of <span class="emphasis"><em>failures</em></span> then we would have taken the floor
instead. We would also have called <code class="computeroutput"><span class="identifier">find_minimum_number_of_trials</span></code>
- like this:
+ like this:
</p>
<pre class="programlisting"><span class="identifier">floor</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">::</span><span class="identifier">find_minimum_number_of_trials</span><span class="special">(</span><span class="identifier">failures</span><span class="special">,</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]))</span>
</pre>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -71,7 +71,6 @@
policy of real, rather than the default policy integer_round_outwards.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_OVERFLOW_ERROR_POLICY</span> <span class="identifier">ignore_error</span>
<span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_DISCRETE_QUANTILE_POLICY</span> <span class="identifier">real</span></pre>
@@ -95,7 +94,6 @@
and we need some std library iostream, of course.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">negative_binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
<span class="comment">// for negative_binomial_distribution</span>
@@ -108,7 +106,7 @@
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">noshowpoint</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">fixed</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">left</span><span class="special">;</span>
<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iomanip</span><span class="special">></span>
- <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">;</span>
+ <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">;</span>
<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">limits</span><span class="special">></span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">;</span>
@@ -124,7 +122,6 @@
error message instead of an abrupt program abort.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">try</span>
<span class="special">{</span></pre>
@@ -136,7 +133,6 @@
this takes is therefore = sucesses + failures or k + r = k + 5.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">sales_quota</span> <span class="special">=</span> <span class="number">5</span><span class="special">;</span> <span class="comment">// Pat's sales quota - successes (r).</span></pre>
<p>
@@ -146,7 +142,6 @@
bar and a 0.6 probability (60%) of selling nothing.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">success_fraction</span> <span class="special">=</span> <span class="number">0.4</span><span class="special">;</span> <span class="comment">// success_fraction (p) - so failure_fraction is 0.6.</span></pre>
<p>
@@ -164,7 +159,6 @@
success.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">negative_binomial</span> <span class="identifier">nb</span><span class="special">(</span><span class="identifier">sales_quota</span><span class="special">,</span> <span class="identifier">success_fraction</span><span class="special">);</span> <span class="comment">// type double by default.</span></pre>
<p>
@@ -174,7 +168,6 @@
of the distribution.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Pat has a sales per house success rate of "</span> <span class="special"><<</span> <span class="identifier">success_fraction</span>
<span class="special"><<</span> <span class="string">".\nTherefore he would, on average, sell "</span> <span class="special"><<</span> <span class="identifier">nb</span><span class="special">.</span><span class="identifier">success_fraction</span><span class="special">()</span> <span class="special">*</span> <span class="number">100</span>
@@ -182,7 +175,7 @@
<span class="keyword">int</span> <span class="identifier">all_houses</span> <span class="special">=</span> <span class="number">30</span><span class="special">;</span> <span class="comment">// The number of houses on the estate.</span>
-<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"With a success rate of "</span> <span class="special"><<</span> <span class="identifier">nb</span><span class="special">.</span><span class="identifier">success_fraction</span><span class="special">()</span>
+<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"With a success rate of "</span> <span class="special"><<</span> <span class="identifier">nb</span><span class="special">.</span><span class="identifier">success_fraction</span><span class="special">()</span>
<span class="special"><<</span> <span class="string">", he might expect, on average,\n"</span>
<span class="string">"to need to visit about "</span> <span class="special"><<</span> <span class="identifier">success_fraction</span> <span class="special">*</span> <span class="identifier">all_houses</span>
<span class="special"><<</span> <span class="string">" houses in order to sell all "</span> <span class="special"><<</span> <span class="identifier">nb</span><span class="special">.</span><span class="identifier">successes</span><span class="special">()</span> <span class="special"><<</span> <span class="string">" bars. "</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span></pre>
@@ -191,7 +184,7 @@
<pre class="programlisting">Pat has a sales per house success rate of 0.4.
Therefore he would, on average, sell 40 bars after trying 100 houses.
With a success rate of 0.4, he might expect, on average,
-to need to visit about 12 houses in order to sell all 5 bars.
+to need to visit about 12 houses in order to sell all 5 bars.
</pre>
<p>
The random variable of interest is the number of houses that must be
@@ -205,7 +198,6 @@
We calculate this using the pdf function:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability that Pat finishes on the "</span> <span class="special"><<</span> <span class="identifier">sales_quota</span> <span class="special"><<</span> <span class="string">"th house is "</span>
<span class="special"><<</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">5</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// == pdf(nb, 0)</span></pre>
@@ -222,7 +214,6 @@
Density Function (pdf).
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability that Pat finishes on the 6th house is "</span>
<span class="special"><<</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">6</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
@@ -241,7 +232,6 @@
Function (cdf). We can calculate it by adding the individual probabilities.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability that Pat finishes on or before the 8th house is sum "</span>
<span class="string">"\n"</span> <span class="special"><<</span> <span class="string">"pdf(sales_quota) + pdf(6) + pdf(7) + pdf(8) = "</span>
@@ -260,7 +250,6 @@
distribution function.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"\nProbability of selling his quota of "</span> <span class="special"><<</span> <span class="identifier">sales_quota</span>
<span class="special"><<</span> <span class="string">" bars\non or before the "</span> <span class="special"><<</span> <span class="number">8</span> <span class="special"><<</span> <span class="string">"th house is "</span>
@@ -270,7 +259,6 @@
<pre class="programlisting">Probability of selling his quota of 5 bars on or before the 8th house is 0.17367
</pre>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"\nProbability that Pat finishes exactly on the 10th house is "</span>
<span class="special"><<</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">10</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
@@ -283,7 +271,6 @@
Probability of selling his quota of 5 bars on or before the 10th house is 0.3669
</pre>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability that Pat finishes exactly on the 11th house is "</span>
<span class="special"><<</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">11</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
@@ -297,7 +284,6 @@
on or before the 11th house is 0.46723
</pre>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability that Pat finishes exactly on the 12th house is "</span>
<span class="special"><<</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">12</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
@@ -318,7 +304,6 @@
would sell all his quota on the very last house.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability that Pat finishes on the "</span> <span class="special"><<</span> <span class="identifier">all_houses</span>
<span class="special"><<</span> <span class="string">" house is "</span> <span class="special"><<</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="identifier">all_houses</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span></pre>
@@ -338,7 +323,6 @@
5 candy bars?
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"\nProbability of selling his quota of "</span> <span class="special"><<</span> <span class="identifier">sales_quota</span>
<span class="special"><<</span> <span class="string">" bars\non or before the "</span> <span class="special"><<</span> <span class="identifier">all_houses</span> <span class="special"><<</span> <span class="string">"th house is "</span>
@@ -380,7 +364,6 @@
of the cdf. <a class="link" href="../../overview/complements.html#why_complements">Why complements?</a>
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"\nProbability of failing to sell his quota of "</span> <span class="special"><<</span> <span class="identifier">sales_quota</span>
<span class="special"><<</span> <span class="string">" bars\neven after visiting all "</span> <span class="special"><<</span> <span class="identifier">all_houses</span> <span class="special"><<</span> <span class="string">" houses is "</span>
@@ -395,16 +378,14 @@
to predict which house Pat will finish on. So for the 8th house:
</p>
<p>
-
</p>
-<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="special">(</span><span class="number">8</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">));</span>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="special">(</span><span class="number">8</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">));</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability of meeting sales quota on or before 8th house is "</span><span class="special"><<</span> <span class="identifier">p</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span></pre>
<p>
</p>
<pre class="programlisting">Probability of meeting sales quota on or before 8th house is 0.174
</pre>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"If the confidence of meeting sales quota is "</span> <span class="special"><<</span> <span class="identifier">p</span>
<span class="special"><<</span> <span class="string">", then the finishing house is "</span> <span class="special"><<</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="identifier">p</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">sales_quota</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
@@ -421,7 +402,6 @@
his quota).
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"If the confidence of meeting sales quota is "</span> <span class="special"><<</span> <span class="number">1.</span>
<span class="special"><<</span> <span class="string">", then the finishing house is "</span> <span class="special"><<</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">1</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">sales_quota</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
@@ -434,7 +414,6 @@
And similarly for a few other probabilities:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"If the confidence of meeting sales quota is "</span> <span class="special"><<</span> <span class="number">0.</span>
<span class="special"><<</span> <span class="string">", then the finishing house is "</span> <span class="special"><<</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">0.</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">sales_quota</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
@@ -460,9 +439,8 @@
will be successful sales.
</p>
<p>
-
</p>
-<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"If confidence of meeting quota is zero\n(we assume all houses are successful sales)"</span>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"If confidence of meeting quota is zero\n(we assume all houses are successful sales)"</span>
<span class="string">", then finishing house is "</span> <span class="special"><<</span> <span class="identifier">sales_quota</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span></pre>
<p>
</p>
@@ -473,7 +451,6 @@
We can list quantiles for a few probabilities:
</p>
<p>
-
</p>
<pre class="programlisting"> <span class="keyword">double</span> <span class="identifier">ps</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span><span class="number">0.</span><span class="special">,</span> <span class="number">0.001</span><span class="special">,</span> <span class="number">0.01</span><span class="special">,</span> <span class="number">0.05</span><span class="special">,</span> <span class="number">0.1</span><span class="special">,</span> <span class="number">0.5</span><span class="special">,</span> <span class="number">0.9</span><span class="special">,</span> <span class="number">0.95</span><span class="special">,</span> <span class="number">0.99</span><span class="special">,</span> <span class="number">0.999</span><span class="special">,</span> <span class="number">1.</span><span class="special">};</span>
<span class="comment">// Confidence as fraction = 1-alpha, as percent = 100 * (1-alpha[i]) %</span>
@@ -500,14 +477,14 @@
</pre>
<p>
We could have applied a ceil function to obtain a 'worst case' integer
- value for house.
+ value for house.
</p>
<pre class="programlisting"><span class="identifier">ceil</span><span class="special">(</span><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="identifier">ps</span><span class="special">[</span><span class="identifier">i</span><span class="special">]))</span></pre>
<p>
</p>
<p>
Or, if we had used the default discrete quantile policy, integer_outside,
- by omitting
+ by omitting
</p>
<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_DISCRETE_QUANTILE_POLICY</span> <span class="identifier">real</span></pre>
<p>
@@ -530,7 +507,6 @@
on each house.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"\nHouse for "</span> <span class="special"><<</span> <span class="identifier">sales_quota</span> <span class="special"><<</span> <span class="string">"th (last) sale. Probability (%)"</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="number">5</span><span class="special">);</span>
@@ -542,31 +518,31 @@
<p>
</p>
<pre class="programlisting">House for 5 th (last) sale. Probability (%)
-5 0.01024
-6 0.04096
+5 0.01024
+6 0.04096
7 0.096256
-8 0.17367
-9 0.26657
-10 0.3669
-11 0.46723
-12 0.56182
-13 0.64696
-14 0.72074
-15 0.78272
-16 0.83343
-17 0.874
-18 0.90583
-19 0.93039
-20 0.94905
-21 0.96304
-22 0.97342
-23 0.98103
-24 0.98655
-25 0.99053
-26 0.99337
-27 0.99539
-28 0.99681
-29 0.9978
+8 0.17367
+9 0.26657
+10 0.3669
+11 0.46723
+12 0.56182
+13 0.64696
+14 0.72074
+15 0.78272
+16 0.83343
+17 0.874
+18 0.90583
+19 0.93039
+20 0.94905
+21 0.96304
+22 0.97342
+23 0.98103
+24 0.98655
+25 0.99053
+26 0.99337
+27 0.99539
+28 0.99681
+29 0.9978
30 0.99849
</pre>
<p>
@@ -574,7 +550,6 @@
you do not expect to use it.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="special">}</span>
<span class="keyword">catch</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exception</span><span class="special">&</span> <span class="identifier">e</span><span class="special">)</span>
@@ -585,7 +560,6 @@
</p>
<p>
For example, without a ignore domain error policy, if we asked for
-
</p>
<pre class="programlisting"><span class="identifier">pdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="special">-</span><span class="number">1</span><span class="special">)</span></pre>
<p>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -32,7 +32,6 @@
for various k failures.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="comment">// Print a table of values that can be used to plot</span>
<span class="comment">// using Excel, or some other superior graphical display tool.</span>
@@ -56,73 +55,72 @@
<p>
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">k</span> <span class="identifier">pdf</span> <span class="identifier">cdf</span>
- <span class="number">0</span><span class="special">,</span> <span class="number">1.5258789062500000e-005</span> <span class="number">1.5258789062500003e-005</span>
- <span class="number">1</span><span class="special">,</span> <span class="number">9.1552734375000000e-005</span> <span class="number">0.00010681152343750000</span>
- <span class="number">2</span><span class="special">,</span> <span class="number">0.00030899047851562522</span> <span class="number">0.00041580200195312500</span>
- <span class="number">3</span><span class="special">,</span> <span class="number">0.00077247619628906272</span> <span class="number">0.0011882781982421875</span>
- <span class="number">4</span><span class="special">,</span> <span class="number">0.0015932321548461918</span> <span class="number">0.0027815103530883789</span>
- <span class="number">5</span><span class="special">,</span> <span class="number">0.0028678178787231476</span> <span class="number">0.0056493282318115234</span>
- <span class="number">6</span><span class="special">,</span> <span class="number">0.0046602040529251142</span> <span class="number">0.010309532284736633</span>
- <span class="number">7</span><span class="special">,</span> <span class="number">0.0069903060793876605</span> <span class="number">0.017299838364124298</span>
- <span class="number">8</span><span class="special">,</span> <span class="number">0.0098301179241389001</span> <span class="number">0.027129956288263202</span>
- <span class="number">9</span><span class="special">,</span> <span class="number">0.013106823898851871</span> <span class="number">0.040236780187115073</span>
-<span class="number">10</span><span class="special">,</span> <span class="number">0.016711200471036140</span> <span class="number">0.056947980658151209</span>
-<span class="number">11</span><span class="special">,</span> <span class="number">0.020509200578089786</span> <span class="number">0.077457181236241013</span>
-<span class="number">12</span><span class="special">,</span> <span class="number">0.024354675686481652</span> <span class="number">0.10181185692272265</span>
-<span class="number">13</span><span class="special">,</span> <span class="number">0.028101548869017230</span> <span class="number">0.12991340579173993</span>
-<span class="number">14</span><span class="special">,</span> <span class="number">0.031614242477644432</span> <span class="number">0.16152764826938440</span>
-<span class="number">15</span><span class="special">,</span> <span class="number">0.034775666725408917</span> <span class="number">0.19630331499479325</span>
-<span class="number">16</span><span class="special">,</span> <span class="number">0.037492515688331451</span> <span class="number">0.23379583068312471</span>
-<span class="number">17</span><span class="special">,</span> <span class="number">0.039697957787645101</span> <span class="number">0.27349378847076977</span>
-<span class="number">18</span><span class="special">,</span> <span class="number">0.041352039362130305</span> <span class="number">0.31484582783290005</span>
-<span class="number">19</span><span class="special">,</span> <span class="number">0.042440250924291580</span> <span class="number">0.35728607875719176</span>
-<span class="number">20</span><span class="special">,</span> <span class="number">0.042970754060845245</span> <span class="number">0.40025683281803687</span>
-<span class="number">21</span><span class="special">,</span> <span class="number">0.042970754060845225</span> <span class="number">0.44322758687888220</span>
-<span class="number">22</span><span class="special">,</span> <span class="number">0.042482450037426581</span> <span class="number">0.48571003691630876</span>
-<span class="number">23</span><span class="special">,</span> <span class="number">0.041558918514873783</span> <span class="number">0.52726895543118257</span>
-<span class="number">24</span><span class="special">,</span> <span class="number">0.040260202311284021</span> <span class="number">0.56752915774246648</span>
-<span class="number">25</span><span class="special">,</span> <span class="number">0.038649794218832620</span> <span class="number">0.60617895196129912</span>
-<span class="number">26</span><span class="special">,</span> <span class="number">0.036791631035234917</span> <span class="number">0.64297058299653398</span>
-<span class="number">27</span><span class="special">,</span> <span class="number">0.034747651533277427</span> <span class="number">0.67771823452981139</span>
-<span class="number">28</span><span class="special">,</span> <span class="number">0.032575923312447595</span> <span class="number">0.71029415784225891</span>
-<span class="number">29</span><span class="special">,</span> <span class="number">0.030329307911589130</span> <span class="number">0.74062346575384819</span>
-<span class="number">30</span><span class="special">,</span> <span class="number">0.028054609818219924</span> <span class="number">0.76867807557206813</span>
-<span class="number">31</span><span class="special">,</span> <span class="number">0.025792141284492545</span> <span class="number">0.79447021685656061</span>
-<span class="number">32</span><span class="special">,</span> <span class="number">0.023575629142856460</span> <span class="number">0.81804584599941710</span>
-<span class="number">33</span><span class="special">,</span> <span class="number">0.021432390129869489</span> <span class="number">0.83947823612928651</span>
-<span class="number">34</span><span class="special">,</span> <span class="number">0.019383705779220189</span> <span class="number">0.85886194190850684</span>
-<span class="number">35</span><span class="special">,</span> <span class="number">0.017445335201298231</span> <span class="number">0.87630727710980494</span>
-<span class="number">36</span><span class="special">,</span> <span class="number">0.015628112784496322</span> <span class="number">0.89193538989430121</span>
-<span class="number">37</span><span class="special">,</span> <span class="number">0.013938587078064250</span> <span class="number">0.90587397697236549</span>
-<span class="number">38</span><span class="special">,</span> <span class="number">0.012379666154859701</span> <span class="number">0.91825364312722524</span>
-<span class="number">39</span><span class="special">,</span> <span class="number">0.010951243136991251</span> <span class="number">0.92920488626421649</span>
-<span class="number">40</span><span class="special">,</span> <span class="number">0.0096507830144735539</span> <span class="number">0.93885566927869002</span>
-<span class="number">41</span><span class="special">,</span> <span class="number">0.0084738582566109364</span> <span class="number">0.94732952753530097</span>
-<span class="number">42</span><span class="special">,</span> <span class="number">0.0074146259745345548</span> <span class="number">0.95474415350983555</span>
-<span class="number">43</span><span class="special">,</span> <span class="number">0.0064662435824429246</span> <span class="number">0.96121039709227851</span>
-<span class="number">44</span><span class="special">,</span> <span class="number">0.0056212231142827853</span> <span class="number">0.96683162020656122</span>
-<span class="number">45</span><span class="special">,</span> <span class="number">0.0048717266990450708</span> <span class="number">0.97170334690560634</span>
-<span class="number">46</span><span class="special">,</span> <span class="number">0.0042098073105878630</span> <span class="number">0.97591315421619418</span>
-<span class="number">47</span><span class="special">,</span> <span class="number">0.0036275999165703964</span> <span class="number">0.97954075413276465</span>
-<span class="number">48</span><span class="special">,</span> <span class="number">0.0031174686783026818</span> <span class="number">0.98265822281106729</span>
-<span class="number">49</span><span class="special">,</span> <span class="number">0.0026721160099737302</span> <span class="number">0.98533033882104104</span>
-<span class="number">50</span><span class="special">,</span> <span class="number">0.0022846591885275322</span> <span class="number">0.98761499800956853</span>
-<span class="number">51</span><span class="special">,</span> <span class="number">0.0019486798960970148</span> <span class="number">0.98956367790566557</span>
-<span class="number">52</span><span class="special">,</span> <span class="number">0.0016582516423517923</span> <span class="number">0.99122192954801736</span>
-<span class="number">53</span><span class="special">,</span> <span class="number">0.0014079495076571762</span> <span class="number">0.99262987905567457</span>
-<span class="number">54</span><span class="special">,</span> <span class="number">0.0011928461106539983</span> <span class="number">0.99382272516632852</span>
-<span class="number">55</span><span class="special">,</span> <span class="number">0.0010084971662802015</span> <span class="number">0.99483122233260868</span>
-<span class="number">56</span><span class="special">,</span> <span class="number">0.00085091948404891532</span> <span class="number">0.99568214181665760</span>
-<span class="number">57</span><span class="special">,</span> <span class="number">0.00071656377604119542</span> <span class="number">0.99639870559269883</span>
-<span class="number">58</span><span class="special">,</span> <span class="number">0.00060228420831048650</span> <span class="number">0.99700098980100937</span>
-<span class="number">59</span><span class="special">,</span> <span class="number">0.00050530624256557675</span> <span class="number">0.99750629604357488</span>
-<span class="number">60</span><span class="special">,</span> <span class="number">0.00042319397814867202</span> <span class="number">0.99792949002172360</span>
-<span class="number">61</span><span class="special">,</span> <span class="number">0.00035381791615708398</span> <span class="number">0.99828330793788067</span>
-<span class="number">62</span><span class="special">,</span> <span class="number">0.00029532382517950324</span> <span class="number">0.99857863176306016</span>
-<span class="number">63</span><span class="special">,</span> <span class="number">0.00024610318764958566</span> <span class="number">0.99882473495070978</span>
+ <span class="number">0</span><span class="special">,</span> <span class="number">1.5258789062500000e-005</span> <span class="number">1.5258789062500003e-005</span>
+ <span class="number">1</span><span class="special">,</span> <span class="number">9.1552734375000000e-005</span> <span class="number">0.00010681152343750000</span>
+ <span class="number">2</span><span class="special">,</span> <span class="number">0.00030899047851562522</span> <span class="number">0.00041580200195312500</span>
+ <span class="number">3</span><span class="special">,</span> <span class="number">0.00077247619628906272</span> <span class="number">0.0011882781982421875</span>
+ <span class="number">4</span><span class="special">,</span> <span class="number">0.0015932321548461918</span> <span class="number">0.0027815103530883789</span>
+ <span class="number">5</span><span class="special">,</span> <span class="number">0.0028678178787231476</span> <span class="number">0.0056493282318115234</span>
+ <span class="number">6</span><span class="special">,</span> <span class="number">0.0046602040529251142</span> <span class="number">0.010309532284736633</span>
+ <span class="number">7</span><span class="special">,</span> <span class="number">0.0069903060793876605</span> <span class="number">0.017299838364124298</span>
+ <span class="number">8</span><span class="special">,</span> <span class="number">0.0098301179241389001</span> <span class="number">0.027129956288263202</span>
+ <span class="number">9</span><span class="special">,</span> <span class="number">0.013106823898851871</span> <span class="number">0.040236780187115073</span>
+<span class="number">10</span><span class="special">,</span> <span class="number">0.016711200471036140</span> <span class="number">0.056947980658151209</span>
+<span class="number">11</span><span class="special">,</span> <span class="number">0.020509200578089786</span> <span class="number">0.077457181236241013</span>
+<span class="number">12</span><span class="special">,</span> <span class="number">0.024354675686481652</span> <span class="number">0.10181185692272265</span>
+<span class="number">13</span><span class="special">,</span> <span class="number">0.028101548869017230</span> <span class="number">0.12991340579173993</span>
+<span class="number">14</span><span class="special">,</span> <span class="number">0.031614242477644432</span> <span class="number">0.16152764826938440</span>
+<span class="number">15</span><span class="special">,</span> <span class="number">0.034775666725408917</span> <span class="number">0.19630331499479325</span>
+<span class="number">16</span><span class="special">,</span> <span class="number">0.037492515688331451</span> <span class="number">0.23379583068312471</span>
+<span class="number">17</span><span class="special">,</span> <span class="number">0.039697957787645101</span> <span class="number">0.27349378847076977</span>
+<span class="number">18</span><span class="special">,</span> <span class="number">0.041352039362130305</span> <span class="number">0.31484582783290005</span>
+<span class="number">19</span><span class="special">,</span> <span class="number">0.042440250924291580</span> <span class="number">0.35728607875719176</span>
+<span class="number">20</span><span class="special">,</span> <span class="number">0.042970754060845245</span> <span class="number">0.40025683281803687</span>
+<span class="number">21</span><span class="special">,</span> <span class="number">0.042970754060845225</span> <span class="number">0.44322758687888220</span>
+<span class="number">22</span><span class="special">,</span> <span class="number">0.042482450037426581</span> <span class="number">0.48571003691630876</span>
+<span class="number">23</span><span class="special">,</span> <span class="number">0.041558918514873783</span> <span class="number">0.52726895543118257</span>
+<span class="number">24</span><span class="special">,</span> <span class="number">0.040260202311284021</span> <span class="number">0.56752915774246648</span>
+<span class="number">25</span><span class="special">,</span> <span class="number">0.038649794218832620</span> <span class="number">0.60617895196129912</span>
+<span class="number">26</span><span class="special">,</span> <span class="number">0.036791631035234917</span> <span class="number">0.64297058299653398</span>
+<span class="number">27</span><span class="special">,</span> <span class="number">0.034747651533277427</span> <span class="number">0.67771823452981139</span>
+<span class="number">28</span><span class="special">,</span> <span class="number">0.032575923312447595</span> <span class="number">0.71029415784225891</span>
+<span class="number">29</span><span class="special">,</span> <span class="number">0.030329307911589130</span> <span class="number">0.74062346575384819</span>
+<span class="number">30</span><span class="special">,</span> <span class="number">0.028054609818219924</span> <span class="number">0.76867807557206813</span>
+<span class="number">31</span><span class="special">,</span> <span class="number">0.025792141284492545</span> <span class="number">0.79447021685656061</span>
+<span class="number">32</span><span class="special">,</span> <span class="number">0.023575629142856460</span> <span class="number">0.81804584599941710</span>
+<span class="number">33</span><span class="special">,</span> <span class="number">0.021432390129869489</span> <span class="number">0.83947823612928651</span>
+<span class="number">34</span><span class="special">,</span> <span class="number">0.019383705779220189</span> <span class="number">0.85886194190850684</span>
+<span class="number">35</span><span class="special">,</span> <span class="number">0.017445335201298231</span> <span class="number">0.87630727710980494</span>
+<span class="number">36</span><span class="special">,</span> <span class="number">0.015628112784496322</span> <span class="number">0.89193538989430121</span>
+<span class="number">37</span><span class="special">,</span> <span class="number">0.013938587078064250</span> <span class="number">0.90587397697236549</span>
+<span class="number">38</span><span class="special">,</span> <span class="number">0.012379666154859701</span> <span class="number">0.91825364312722524</span>
+<span class="number">39</span><span class="special">,</span> <span class="number">0.010951243136991251</span> <span class="number">0.92920488626421649</span>
+<span class="number">40</span><span class="special">,</span> <span class="number">0.0096507830144735539</span> <span class="number">0.93885566927869002</span>
+<span class="number">41</span><span class="special">,</span> <span class="number">0.0084738582566109364</span> <span class="number">0.94732952753530097</span>
+<span class="number">42</span><span class="special">,</span> <span class="number">0.0074146259745345548</span> <span class="number">0.95474415350983555</span>
+<span class="number">43</span><span class="special">,</span> <span class="number">0.0064662435824429246</span> <span class="number">0.96121039709227851</span>
+<span class="number">44</span><span class="special">,</span> <span class="number">0.0056212231142827853</span> <span class="number">0.96683162020656122</span>
+<span class="number">45</span><span class="special">,</span> <span class="number">0.0048717266990450708</span> <span class="number">0.97170334690560634</span>
+<span class="number">46</span><span class="special">,</span> <span class="number">0.0042098073105878630</span> <span class="number">0.97591315421619418</span>
+<span class="number">47</span><span class="special">,</span> <span class="number">0.0036275999165703964</span> <span class="number">0.97954075413276465</span>
+<span class="number">48</span><span class="special">,</span> <span class="number">0.0031174686783026818</span> <span class="number">0.98265822281106729</span>
+<span class="number">49</span><span class="special">,</span> <span class="number">0.0026721160099737302</span> <span class="number">0.98533033882104104</span>
+<span class="number">50</span><span class="special">,</span> <span class="number">0.0022846591885275322</span> <span class="number">0.98761499800956853</span>
+<span class="number">51</span><span class="special">,</span> <span class="number">0.0019486798960970148</span> <span class="number">0.98956367790566557</span>
+<span class="number">52</span><span class="special">,</span> <span class="number">0.0016582516423517923</span> <span class="number">0.99122192954801736</span>
+<span class="number">53</span><span class="special">,</span> <span class="number">0.0014079495076571762</span> <span class="number">0.99262987905567457</span>
+<span class="number">54</span><span class="special">,</span> <span class="number">0.0011928461106539983</span> <span class="number">0.99382272516632852</span>
+<span class="number">55</span><span class="special">,</span> <span class="number">0.0010084971662802015</span> <span class="number">0.99483122233260868</span>
+<span class="number">56</span><span class="special">,</span> <span class="number">0.00085091948404891532</span> <span class="number">0.99568214181665760</span>
+<span class="number">57</span><span class="special">,</span> <span class="number">0.00071656377604119542</span> <span class="number">0.99639870559269883</span>
+<span class="number">58</span><span class="special">,</span> <span class="number">0.00060228420831048650</span> <span class="number">0.99700098980100937</span>
+<span class="number">59</span><span class="special">,</span> <span class="number">0.00050530624256557675</span> <span class="number">0.99750629604357488</span>
+<span class="number">60</span><span class="special">,</span> <span class="number">0.00042319397814867202</span> <span class="number">0.99792949002172360</span>
+<span class="number">61</span><span class="special">,</span> <span class="number">0.00035381791615708398</span> <span class="number">0.99828330793788067</span>
+<span class="number">62</span><span class="special">,</span> <span class="number">0.00029532382517950324</span> <span class="number">0.99857863176306016</span>
+<span class="number">63</span><span class="special">,</span> <span class="number">0.00024610318764958566</span> <span class="number">0.99882473495070978</span>
</pre>
<p>
</p>
Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html 2011-12-21 11:07:37 EST (Wed, 21 Dec 2011)
@@ -31,9 +31,9 @@
The sample program normal_misc_examples.cpp
illustrates their use.
</p>
-<a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.traditional_tables"></a><h5>
-<a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.traditional_tables-heading"></a>
- <a class="link" href="normal_misc.html#math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.traditional_tables">Traditional
+<h5>
+<a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.h0"></a>
+ <span><a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.traditional_tables"></a></span><a class="link" href="normal_misc.html#math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.traditional_tables">Traditional
Tables</a>
</h5>
<p>
@@ -41,7 +41,6 @@
some std output of course).
</p>
<p>
-
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> <span class="comment">// for normal_distribution</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">normal</span><span class="special">;</span> <span class="comment">// typedef provides default type is double.</span>
@@ -66,7 +65,6 @@
Let's start by printing some traditional tables.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">step</span> <span class="special">=</span> <span class="number">1.</span><span class="special">;</span> <span class="comment">// in z </span>
<span class="keyword">double</span> <span class="identifier">range</span> <span class="special">=</span> <span class="number">4</span><span class="special">;</span> <span class="comment">// min and max z = -range to +range.</span>
@@ -86,14 +84,13 @@
First the probability distribution function (pdf).
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Probability distribution function values"</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">" z "</span> <span class="string">" pdf "</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="number">5</span><span class="special">);</span>
<span class="keyword">for</span> <span class="special">(</span><span class="keyword">double</span> <span class="identifier">z</span> <span class="special">=</span> <span class="special">-</span><span class="identifier">range</span><span class="special">;</span> <span class="identifier">z</span> <span class="special"><</span> <span class="identifier">range</span> <span class="special">+</span> <span class="identifier">step</span><span class="special">;</span> <span class="identifier">z</span> <span class="special">+=</span> <span class="identifier">step</span><span class="special">)</span>
<span class="special">{</span>
- <span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">left</span> <span class="special"><<</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">6</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">z</span> <span class="special"><<</span> <span class="string">" "</span>
+ <span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">left</span> <span class="special"><<</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">6</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">z</span> <span class="special"><<</span> <span class="string">" "</span>
<span class="special"><<</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">precision</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">12</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="special">}</span>
<span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="number">6</span><span class="special">);</span> <span class="comment">// default</span></pre>
@@ -104,7 +101,6 @@
function (cdf).
</p>
<p>
-
</p>
<pre class="programlisting"><span class="comment">// For a standard normal distribution </span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Standard normal mean = "</span><span class="special"><<</span> <span class="identifier">s</span><span class="special">.</span><span class="identifier">mean</span><span class="special">()</span>
@@ -113,7 +109,7 @@
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">" z "</span> <span class="string">" cdf "</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">for</span> <span class="special">(</span><span class="keyword">double</span> <span class="identifier">z</span> <span class="special">=</span> <span class="special">-</span><span class="identifier">range</span><span class="special">;</span> <span class="identifier">z</span> <span class="special"><</span> <span class="identifier">range</span> <span class="special">+</span> <span class="identifier">step</span><span class="special">;</span> <span class="identifier">z</span> <span class="special">+=</span> <span class="identifier">step</span><span class="special">)</span>
<span class="special">{</span>
- <span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">left</span> <span class="special"><<</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">6</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">z</span> <span class="special"><<</span> <span class="string">" "</span>
+ <span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">left</span> <span class="special"><<</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">6</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">z</span> <span class="special"><<</span> <span class="string">" "</span>
<span class="special"><<</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">precision</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">12</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="special">}</span>
<span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="number">6</span><span class="special">);</span> <span class="comment">// default</span></pre>
@@ -136,9 +132,8 @@
write
</p>
<p>
-
</p>
-<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">z</span> <span class="special">=</span> <span class="number">2.</span><span class="special">;</span>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">z</span> <span class="special">=</span> <span class="number">2.</span><span class="special">;</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Area for z = "</span> <span class="special"><<</span> <span class="identifier">z</span> <span class="special"><<</span> <span class="string">" is "</span> <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// to get the area for z.</span></pre>
<p>
</p>
@@ -149,7 +144,6 @@
so we can write
</p>
<p>
-
</p>
<pre class="programlisting"> <span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"95% of area has a z below "</span> <span class="special"><<</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="number">0.95</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="comment">// 95% of area has a z below 1.64485</span></pre>
@@ -160,7 +154,6 @@
a one-sided test)
</p>
<p>
-
</p>
<pre class="programlisting"> <span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"95% of area has a z between "</span> <span class="special"><<</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="number">0.975</span><span class="special">)</span>
<span class="special"><<</span> <span class="string">" and "</span> <span class="special"><<</span> <span class="special">-</span><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="number">0.975</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
@@ -177,7 +170,6 @@
neat number like 0.05, but we can easily calculate it,
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">alpha1</span> <span class="special">=</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="special">-</span><span class="number">1</span><span class="special">)</span> <span class="special">*</span> <span class="number">2</span><span class="special">;</span> <span class="comment">// 0.3173105078629142</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">17</span><span class="special">)</span> <span class="special"><<</span> <span class="string">"Significance level for z == 1 is "</span> <span class="special"><<</span> <span class="identifier">alpha1</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span></pre>
@@ -187,7 +179,6 @@
and place in our array of favorite alpha values.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">alpha</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span><span class="number">0.3173105078629142</span><span class="special">,</span> <span class="comment">// z for 1 standard deviation.</span>
<span class="number">0.20</span><span class="special">,</span> <span class="number">0.1</span><span class="special">,</span> <span class="number">0.05</span><span class="special">,</span> <span class="number">0.01</span><span class="special">,</span> <span class="number">0.001</span><span class="special">,</span> <span class="number">0.0001</span><span class="special">,</span> <span class="number">0.00001</span> <span class="special">};</span></pre>
@@ -199,7 +190,6 @@
the calculated interval.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"level of significance (alpha)"</span> <span class="special"><<</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">4</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"2-sided 1 -sided z(alpha) "</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
@@ -229,9 +219,9 @@
the area between -1.96 up to 12.96 is alpha = 0.95. and the sum of
the two tails is 0.025 + 0.025 = 0.05,
</p>
-<a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.standard_deviations_either_side_of_the_mean"></a><h5>
-<a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.standard_deviations_either_side_of_the_mean-heading"></a>
- <a class="link" href="normal_misc.html#math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.standard_deviations_either_side_of_the_mean">Standard
+<h5>
+<a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.h1"></a>
+ <span><a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.standard_deviations_either_side_of_the_mean"></a></span><a class="link" href="normal_misc.html#math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.standard_deviations_either_side_of_the_mean">Standard
deviations either side of the Mean</a>
</h5>
<p>
@@ -240,7 +230,6 @@
3 standard deviations from the mean.
</p>
<p>
-
</p>
<pre class="programlisting"><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="number">3</span><span class="special">);</span>
<span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">showpoint</span> <span class="special"><<</span> <span class="string">"cdf(s, s.standard_deviation()) = "</span>
@@ -279,14 +268,14 @@
deviation</strong></span> are surprisingly wide, especially if you have
estimated the standard deviation from only a few measurements.
</p>
-<a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.some_simple_examples"></a><h5>
-<a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.some_simple_examples-heading"></a>
- <a class="link" href="normal_misc.html#math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.some_simple_examples">Some
+<h5>
+<a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.h2"></a>
+ <span><a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.some_simple_examples"></a></span><a class="link" href="normal_misc.html#math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.some_simple_examples">Some
simple examples</a>
</h5>
-<a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.life_of_light_bulbs"></a><h5>
-<a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.life_of_light_bulbs-heading"></a>
- <a class="link" href="normal_misc.html#math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.life_of_light_bulbs">Life
+<h5>
+<a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.h3"></a>
+ <span><a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.life_of_light_bulbs"></a></span><a class="link" href="normal_misc.html#math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.life_of_light_bulbs">Life
of light bulbs</a>
</h5>
<p>
@@ -298,7 +287,6 @@
A few very simple examples are shown here:
</p>
<p>
-
</p>
<pre class="programlisting"><span class="comment">// K. Krishnamoorthy, Handbook of Statistical Distributions with Applications,</span>
<span class="comment">// ISBN 1 58488 635 8, page 125, example 10.3.5</span></pre>
@@ -311,11 +299,10 @@
<span class="emphasis"><em>bulbs</em></span> with these values: