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Subject: [Boost-commit] svn:boost r67231 - in trunk: boost/math/distributions boost/math/policies boost/math/special_functions libs/math/doc/sf_and_dist libs/math/doc/sf_and_dist/html libs/math/doc/sf_and_dist/html/math_toolkit 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 libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview 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 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 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 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/next_float libs/math/doc/sf_and_dist/html/math_toolkit/utils/rounding libs/math/example libs/math/test
From: john_at_[hidden]
Date: 2010-12-14 14:23:29

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Author: johnmaddock
Date: 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
New Revision: 67231
URL: http://svn.boost.org/trac/boost/changeset/67231

Log:
Improve performance of non-central T by simplifying the arithmetic where possible.
Change error handlers to pass the target type down to "rounding errors".
Change the rounding error handlers to return a well defined value (the maximum representable value in the target type).
Update and complete docs on rounding errors.
Fix typo in test/test_beta_dist.cpp.
Regenerate the docs.
Remove illegal comment from test_constants.cpp.
Fixes #4977.
Text files modified:
   trunk/boost/math/distributions/non_central_beta.hpp | 43
   trunk/boost/math/distributions/non_central_t.hpp | 159 +
   trunk/boost/math/policies/error_handling.hpp | 28
   trunk/boost/math/special_functions/round.hpp | 8
   trunk/boost/math/special_functions/trunc.hpp | 8
   trunk/libs/math/doc/sf_and_dist/error_handling.qbk | 6
   trunk/libs/math/doc/sf_and_dist/html/index.html | 529 ++++----
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders.html | 13
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html | 36
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html | 12
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html | 8
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html | 9
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html | 18
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist.html | 253 ++--
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html | 97
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html | 8
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html | 91
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html | 14
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html | 24
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html | 82
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html | 12
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html | 16
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html | 12
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html | 10
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html | 12
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html | 10
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/geometric_dist.html | 81
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html | 14
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html | 14
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html | 12
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html | 14
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html | 12
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html | 12
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html | 12
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html | 12
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html | 16
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html | 18
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html | 12
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html | 83
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html | 10
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html | 15
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html | 64
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html | 14
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html | 14
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html | 14
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/uniform_dist.html | 12
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/weibull_dist.html | 14
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/nmp.html | 56
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/future.html | 10
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html | 152 +-
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview.html | 21
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.html | 14
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/generic.html | 8
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/headers.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/objects.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/parameters.html | 4
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/summary.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/variates.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg.html | 126 +-
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html | 19
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html | 5
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html | 4
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html | 265 +++-
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html | 500 ++++++--
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/c_sharp.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg.html | 15
   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/cs_eg/chi_sq_size.html | 5
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html | 4
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html | 336 +++--
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html | 144 +
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg.html | 14
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html | 186 ++-
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html | 682 +++++++----
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html | 217 ++-
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nag_library.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg.html | 6
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html | 2278 ++++++++++++++++++++-------------------
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg.html | 20
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html | 103 +
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html | 87
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html | 653 +++++++----
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html | 16
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example.html | 6
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html | 578 ++++++---
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg.html | 26
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/paired_st.html | 4
   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 | 6
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html | 4
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html | 4
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/extern_c.html | 8
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/extern_c/c99.html | 6
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html | 518 +++++---
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html | 8
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview.html | 40
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/FAQ.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/building.html | 8
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html | 1073 +++++++++---------
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/config_macros.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/contact.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html | 6
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html | 34
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html | 507 +++++---
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html | 8
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/namespaces.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html | 4
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/perf_over.html | 70
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/pol_overview.html | 142 +-
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/result_type.html | 4
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/threads.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/tr1.html | 520 +++++---
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/perf.html | 18
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/perf/comp_compilers.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html | 58
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/perf/interp.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/perf/perf_over.html | 70
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/perf/perf_test_app.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/perf/tuning.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy.html | 66
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_overview.html | 142 +-
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref.html | 22
   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 | 38
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html | 30
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html | 16
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/iteration_pol.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/namespace_pol.html | 14
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/pol_ref_ref.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html | 34
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/precision_pol.html | 20
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial.html | 38
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html | 10
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html | 16
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/changing_policy_defaults.html | 145 +
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/namespace_policies.html | 248 ++-
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_tut_defaults.html | 4
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_usage.html | 4
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html | 68
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/user_def_err_pol.html | 395 ++++--
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/what_is_a_policy.html | 4
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special.html | 133 +-
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel.html | 20
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html | 23
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html | 8
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html | 23
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html | 25
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint.html | 12
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html | 34
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html | 34
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html | 38
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html | 56
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html | 14
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/expint.html | 10
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html | 29
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html | 25
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials.html | 18
   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 | 21
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html | 23
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html | 21
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html | 21
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html | 10
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html | 19
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html | 19
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html | 19
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers.html | 16
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html | 17
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html | 27
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html | 17
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html | 15
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html | 17
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html | 17
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html | 17
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html | 10
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html | 21
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html | 23
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html | 23
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html | 89 +
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf.html | 7
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html | 24
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html | 23
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma.html | 16
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html | 23
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_derivatives.html | 21
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html | 32
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html | 25
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html | 23
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html | 23
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html | 34
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html | 10
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html | 23
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html | 23
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html | 23
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html | 23
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc.html | 4
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html | 11
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinhc_pi.html | 11
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/zetas.html | 4
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html | 23
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/status.html | 8
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/status/credits.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/status/history1.html | 507 +++++---
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/status/issues.html | 18
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit.html | 34
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1.html | 20
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html | 10
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/constants.html | 6
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html | 8
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html | 8
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html | 26
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html | 47
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html | 10
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/tuples.html | 6
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2.html | 10
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html | 8
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html | 6
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html | 16
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals_overview.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/using_udt.html | 12
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/using_udt/archetypes.html | 10
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/using_udt/concepts.html | 6
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/using_udt/dist_concept.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/using_udt/use_mpfr.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/using_udt/use_ntl.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils.html | 30
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/fpclass.html | 6
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/next_float.html | 14
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_advance.html | 6
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_distance.html | 6
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_next.html | 8
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_prior.html | 6
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/next_float/nextafter.html | 8
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/rounding.html | 8
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/rounding/modf.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/rounding/round.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/rounding/trunc.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/sign_functions.html | 6
   trunk/libs/math/example/policy_eg_8.cpp | 2
   trunk/libs/math/test/test_beta_dist.cpp | 2
   trunk/libs/math/test/test_constants.cpp | 2
   247 files changed, 8842 insertions(+), 6482 deletions(-)

Modified: trunk/boost/math/distributions/non_central_beta.hpp
==============================================================================
--- trunk/boost/math/distributions/non_central_beta.hpp (original)
+++ trunk/boost/math/distributions/non_central_beta.hpp 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -43,13 +43,25 @@
 T l2 = lam / 2;
 //
 // k is the starting point for iteration, and is the
- // maximum of the poisson weighting term:
+ // maximum of the poisson weighting term,
+ // note that unlike other similar code, we do not set
+ // k to zero, when l2 is small, as forward iteration
+ // is unstable:
 //
 int k = itrunc(l2);
 if(k == 0)
 k = 1;
- // Starting Poisson weight:
- T pois = gamma_p_derivative(T(k+1), l2, pol);
+ T pois;
+ if(k == 0)
+ {
+ // Starting Poisson weight:
+ pois = exp(-l2);
+ }
+ else
+ {
+ // Starting Poisson weight:
+ pois = gamma_p_derivative(T(k+1), l2, pol);
+ }
 if(pois == 0)
 return init_val;
 // recurance term:
@@ -124,10 +136,27 @@
 // maximum of the poisson weighting term:
 //
 int k = itrunc(l2);
+ T pois;
+ if(k <= 30)
+ {
+ //
+ // Might as well start at 0 since we'll likely have this number of terms anyway:
+ //
+ if(a + b > 1)
+ k = 0;
+ else if(k == 0)
+ k = 1;
+ }
 if(k == 0)
- k = 1;
- // Starting Poisson weight:
- T pois = gamma_p_derivative(T(k+1), l2, pol);
+ {
+ // Starting Poisson weight:
+ pois = exp(-l2);
+ }
+ else
+ {
+ // Starting Poisson weight:
+ pois = gamma_p_derivative(T(k+1), l2, pol);
+ }
 if(pois == 0)
 return init_val;
 // recurance term:
@@ -748,7 +777,7 @@
 RealType b = dist.beta();
 RealType d = dist.non_centrality();
 RealType apb = a + b;
- return exp(-d / 2) * a * detail::hypergeometric_2F2(1 + a, apb, a, 1 + apb, d / 2, Policy()) / apb;
+ return exp(-d / 2) * a * detail::hypergeometric_2F2<RealType, Policy>(1 + a, apb, a, 1 + apb, d / 2, Policy()) / apb;
 } // mean

 template <class RealType, class Policy>

Modified: trunk/boost/math/distributions/non_central_t.hpp
==============================================================================
--- trunk/boost/math/distributions/non_central_t.hpp (original)
+++ trunk/boost/math/distributions/non_central_t.hpp 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -41,20 +41,40 @@
 // maximum of the poisson weighting term:
 //
 int k = boost::math::itrunc(d2);
- // Starting Poisson weight:
- T pois = gamma_p_derivative(T(k+1), d2, pol)
- * tgamma_delta_ratio(T(k + 1), T(0.5f))
- * delta / constants::root_two<T>();
+ T pois;
+ if(k < 15)
+ {
+ // Since we'll likely need 30-40 terms anyway, start from zero
+ // since this simplifies the arithmetic, don't go too overboard though
+ // as this is the *unstable* direction:
+ k = 0;
+ // Starting Poisson weight:
+ pois = exp(-d2) * 2 / constants::root_pi<T>();
+ pois *= delta / constants::root_two<T>();
+ }
+ else
+ {
+ // Starting Poisson weight:
+ pois = gamma_p_derivative(T(k+1), d2, pol)
+ * tgamma_delta_ratio(T(k + 1), T(0.5f))
+ * delta / constants::root_two<T>();
+ }
 if(pois == 0)
 return init_val;
- // Recurance term:
- T xterm;
- // Starting beta term:
- T beta = x < y
- ? detail::ibeta_imp(T(k + 1), T(n / 2), x, pol, false, true, &xterm)
- : detail::ibeta_imp(T(n / 2), T(k + 1), y, pol, true, true, &xterm);
-
- xterm *= y / (n / 2 + k);
+ T xterm, beta;
+ // Recurrance & starting beta terms:
+ if(k == 0)
+ {
+ beta = -boost::math::powm1(y, n / 2, pol);
+ xterm = beta > 0.5f ? pow(y, n / 2) : 1 - beta;
+ }
+ else
+ {
+ beta = x < y
+ ? detail::ibeta_imp(T(k + 1), T(n / 2), x, pol, false, true, &xterm)
+ : detail::ibeta_imp(T(n / 2), T(k + 1), y, pol, true, true, &xterm);
+ xterm *= y / (n / 2 + k);
+ }
 T poisf(pois), betaf(beta), xtermf(xterm);
 T sum = init_val;
 if((xterm == 0) && (beta == 0))
@@ -111,66 +131,89 @@
 // maximum of the poisson weighting term:
 //
 int k = boost::math::itrunc(d2);
+ if(k < 30)
+ {
+ // We typically need around 40 terms so may as well start at 0
+ // and gain faster computation of starting conditions:
+ k = 0;
+ }
 // Starting Poisson weight:
- T pois = gamma_p_derivative(T(k+1), d2, pol)
- * tgamma_delta_ratio(T(k + 1), T(0.5f))
- * delta / constants::root_two<T>();
+ T pois;
+ if(k == 0)
+ {
+ pois = exp(-d2) * 2 / constants::root_pi<T>();
+ pois *= delta / constants::root_two<T>();
+ }
+ else if((k < (int)(max_factorial<T>::value)) && (d2 < tools::log_max_value<T>()) && (log(d2) * k < tools::log_max_value<T>()))
+ {
+ //
+ // For small k we can optimise this calculation by using
+ // a simpler reduced formula:
+ //
+ pois = exp(-d2);
+ pois *= pow(d2, static_cast<T>(k));
+ pois /= boost::math::tgamma(T(k + 1 + 0.5), pol);
+ pois *= delta / constants::root_two<T>();
+ }
+ else
+ {
+ pois = gamma_p_derivative(T(k+1), d2, pol)
+ * tgamma_delta_ratio(T(k + 1), T(0.5f))
+ * delta / constants::root_two<T>();
+ }
 if(pois == 0)
 return init_val;
 // Recurance term:
 T xterm;
+ T beta;
 // Starting beta term:
- T beta = x < y
- ? detail::ibeta_imp(T(k + 1), T(n / 2), x, pol, true, true, &xterm)
- : detail::ibeta_imp(T(n / 2), T(k + 1), y, pol, false, true, &xterm);
+ if(k != 0)
+ {
+ beta = x < y
+ ? detail::ibeta_imp(T(k + 1), T(n / 2), x, pol, true, true, &xterm)
+ : detail::ibeta_imp(T(n / 2), T(k + 1), y, pol, false, true, &xterm);

- xterm *= y / (n / 2 + k);
+ xterm *= y / (n / 2 + k);
+ }
+ else
+ {
+ beta = pow(y, n / 2);
+ xterm = beta;
+ }
 T poisf(pois), betaf(beta), xtermf(xterm);
 T sum = init_val;
 if((xterm == 0) && (beta == 0))
 return init_val;

 //
- // Forward recursion first, this is the stable direction:
+ // Fused forward and backwards recursion:
 //
 boost::uintmax_t count = 0;
- for(int i = k + 1; ; ++i)
+ for(int i = k + 1, j = k; ; ++i, --j)
 {
 poisf *= d2 / (i + 0.5f);
 xtermf *= (x * (n / 2 + i - 1)) / (i);
 betaf += xtermf;
-
 T term = poisf * betaf;
- sum += term;
- if(fabs(term/sum) < errtol)
- break;
- if(count > max_iter)
+
+ if(j >= 0)
 {
- return policies::raise_evaluation_error(
- "cdf(non_central_t_distribution<%1%>, %1%)",
- "Series did not converge, closest value was %1%", sum, pol);
+ term += beta * pois;
+ pois *= (j + 0.5f) / d2;
+ beta -= xterm;
+ xterm *= (j) / (x * (n / 2 + j - 1));
 }
- ++count;
- }
- //
- // Backwards recursion:
- //
- for(int i = k; i >= 0; --i)
- {
- T term = beta * pois;
+
 sum += term;
 if(fabs(term/sum) < errtol)
 break;
- pois *= (i + 0.5f) / d2;
- beta -= xterm;
- xterm *= (i) / (x * (n / 2 + i - 1));
- ++count;
 if(count > max_iter)
 {
 return policies::raise_evaluation_error(
 "cdf(non_central_t_distribution<%1%>, %1%)",
 "Series did not converge, closest value was %1%", sum, pol);
 }
+ ++count;
 }
 return sum;
 }
@@ -326,14 +369,32 @@
 // maximum of the poisson weighting term:
 //
 int k = boost::math::itrunc(d2);
- // Starting Poisson weight:
- T pois = gamma_p_derivative(T(k+1), d2, pol)
- * tgamma_delta_ratio(T(k + 1), T(0.5f))
- * delta / constants::root_two<T>();
- // Starting beta term:
- T xterm = x < y
- ? ibeta_derivative(T(k + 1), n / 2, x, pol)
- : ibeta_derivative(n / 2, T(k + 1), y, pol);
+ T pois, xterm;
+ if(k < 30)
+ {
+ //
+ // Since we'll need at least 30-40 terms anyway, start from 0
+ // since this simplifies the starting arithmetic:
+ //
+ k = 0;
+ // Starting Poisson weight:
+ pois = exp(-d2)
+ * (2 / constants::root_pi<T>())
+ * delta / constants::root_two<T>();
+ // Starting beta term:
+ xterm = pow(y, n / 2 - 1) * n / 2;
+ }
+ else
+ {
+ // Starting Poisson weight:
+ pois = gamma_p_derivative(T(k+1), d2, pol)
+ * tgamma_delta_ratio(T(k + 1), T(0.5f))
+ * delta / constants::root_two<T>();
+ // Starting beta term:
+ xterm = x < y
+ ? ibeta_derivative(T(k + 1), n / 2, x, pol)
+ : ibeta_derivative(n / 2, T(k + 1), y, pol);
+ }
 T poisf(pois), xtermf(xterm);
 T sum = init_val;
 if((pois == 0) || (xterm == 0))

Modified: trunk/boost/math/policies/error_handling.hpp
==============================================================================
--- trunk/boost/math/policies/error_handling.hpp (original)
+++ trunk/boost/math/policies/error_handling.hpp 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -60,8 +60,8 @@
T user_denorm_error(const char* function, const char* message, const T& val);
template <class T>
T user_evaluation_error(const char* function, const char* message, const T& val);
-template <class T>
-T user_rounding_error(const char* function, const char* message, const T& val);
+template <class T, class TargetType>
+T user_rounding_error(const char* function, const char* message, const T& val, const TargetType& t);
template <class T>
T user_indeterminate_result_error(const char* function, const char* message, const T& val);

@@ -381,11 +381,12 @@
 return user_evaluation_error(function, message, val);
}

-template <class T>
+template <class T, class TargetType>
inline T raise_rounding_error(
 const char* function,
 const char* message,
 const T& val,
+ const TargetType&,
 const ::boost::math::policies::rounding_error< ::boost::math::policies::throw_on_error>&)
{
 raise_error<boost::math::rounding_error, T>(function, message, val);
@@ -393,39 +394,42 @@
 return T(0);
}

-template <class T>
+template <class T, class TargetType>
inline T raise_rounding_error(
 const char* ,
 const char* ,
 const T& val,
+ const TargetType&,
 const ::boost::math::policies::rounding_error< ::boost::math::policies::ignore_error>&)
{
 // This may or may not do the right thing, but the user asked for the error
 // to be ignored so here we go anyway:
- return val;
+ return std::numeric_limits<T>::is_specialized ? (val > 0 ? std::numeric_limits<T>::max() : -std::numeric_limits<T>::max()): val;
}

-template <class T>
+template <class T, class TargetType>
inline T raise_rounding_error(
 const char* ,
 const char* ,
 const T& val,
+ const TargetType&,
 const ::boost::math::policies::rounding_error< ::boost::math::policies::errno_on_error>&)
{
 errno = ERANGE;
 // This may or may not do the right thing, but the user asked for the error
 // to be silent so here we go anyway:
- return val;
+ return std::numeric_limits<T>::is_specialized ? (val > 0 ? std::numeric_limits<T>::max() : -std::numeric_limits<T>::max()): val;
}

-template <class T>
+template <class T, class TargetType>
inline T raise_rounding_error(
 const char* function,
 const char* message,
 const T& val,
+ const TargetType& t,
 const ::boost::math::policies::rounding_error< ::boost::math::policies::user_error>&)
{
- return user_rounding_error(function, message, val);
+ return user_rounding_error(function, message, val, t);
}

template <class T, class R>
@@ -536,13 +540,13 @@
 val, policy_type());
}

-template <class T, class Policy>
-inline T raise_rounding_error(const char* function, const char* message, const T& val, const Policy&)
+template <class T, class TargetType, class Policy>
+inline T raise_rounding_error(const char* function, const char* message, const T& val, const TargetType& t, const Policy&)
{
 typedef typename Policy::rounding_error_type policy_type;
 return detail::raise_rounding_error(
 function, message ? message : "Value %1% can not be represented in the target integer type.",
- val, policy_type());
+ val, t, policy_type());
}

template <class T, class R, class Policy>

Modified: trunk/boost/math/special_functions/round.hpp
==============================================================================
--- trunk/boost/math/special_functions/round.hpp (original)
+++ trunk/boost/math/special_functions/round.hpp 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -21,7 +21,7 @@
{
 BOOST_MATH_STD_USING
 if(!(boost::math::isfinite)(v))
- return policies::raise_rounding_error("boost::math::round<%1%>(%1%)", 0, v, pol);
+ return policies::raise_rounding_error("boost::math::round<%1%>(%1%)", 0, v, v, pol);
 return v < 0 ? static_cast<T>(ceil(v - 0.5f)) : static_cast<T>(floor(v + 0.5f));
}
template <class T>
@@ -44,7 +44,7 @@
 BOOST_MATH_STD_USING
 T r = boost::math::round(v, pol);
 if(fabs(r) > (std::numeric_limits<int>::max)())
- return static_cast<int>(policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, pol));
+ return static_cast<int>(policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0, pol));
 return static_cast<int>(r);
}
template <class T>
@@ -59,7 +59,7 @@
 BOOST_MATH_STD_USING
 T r = boost::math::round(v, pol);
 if(fabs(r) > (std::numeric_limits<long>::max)())
- return static_cast<long int>(policies::raise_rounding_error("boost::math::lround<%1%>(%1%)", 0, v, pol));
+ return static_cast<long int>(policies::raise_rounding_error("boost::math::lround<%1%>(%1%)", 0, v, 0L, pol));
 return static_cast<long int>(r);
}
template <class T>
@@ -76,7 +76,7 @@
 BOOST_MATH_STD_USING
 T r = boost::math::round(v, pol);
 if(fabs(r) > (std::numeric_limits<boost::long_long_type>::max)())
- return static_cast<boost::long_long_type>(policies::raise_rounding_error("boost::math::llround<%1%>(%1%)", 0, v, pol));
+ return static_cast<boost::long_long_type>(policies::raise_rounding_error("boost::math::llround<%1%>(%1%)", 0, v, 0LL, pol));
 return static_cast<boost::long_long_type>(r);
}
template <class T>

Modified: trunk/boost/math/special_functions/trunc.hpp
==============================================================================
--- trunk/boost/math/special_functions/trunc.hpp (original)
+++ trunk/boost/math/special_functions/trunc.hpp 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -21,7 +21,7 @@
{
 BOOST_MATH_STD_USING
 if(!(boost::math::isfinite)(v))
- return policies::raise_rounding_error("boost::math::trunc<%1%>(%1%)", 0, v, pol);
+ return policies::raise_rounding_error("boost::math::trunc<%1%>(%1%)", 0, v, v, pol);
 return (v >= 0) ? static_cast<T>(floor(v)) : static_cast<T>(ceil(v));
}
template <class T>
@@ -44,7 +44,7 @@
 BOOST_MATH_STD_USING
 T r = boost::math::trunc(v, pol);
 if(fabs(r) > (std::numeric_limits<int>::max)())
- return static_cast<int>(policies::raise_rounding_error("boost::math::itrunc<%1%>(%1%)", 0, v, pol));
+ return static_cast<int>(policies::raise_rounding_error("boost::math::itrunc<%1%>(%1%)", 0, 0, v, pol));
 return static_cast<int>(r);
}
template <class T>
@@ -59,7 +59,7 @@
 BOOST_MATH_STD_USING
 T r = boost::math::trunc(v, pol);
 if(fabs(r) > (std::numeric_limits<long>::max)())
- return static_cast<long>(policies::raise_rounding_error("boost::math::ltrunc<%1%>(%1%)", 0, v, pol));
+ return static_cast<long>(policies::raise_rounding_error("boost::math::ltrunc<%1%>(%1%)", 0, 0L, v, pol));
 return static_cast<long>(r);
}
template <class T>
@@ -76,7 +76,7 @@
 BOOST_MATH_STD_USING
 T r = boost::math::trunc(v, pol);
 if(fabs(r) > (std::numeric_limits<boost::long_long_type>::max)())
- return static_cast<boost::long_long_type>(policies::raise_rounding_error("boost::math::lltrunc<%1%>(%1%)", 0, v, pol));
+ return static_cast<boost::long_long_type>(policies::raise_rounding_error("boost::math::lltrunc<%1%>(%1%)", 0, v, 0LL, pol));
 return static_cast<boost::long_long_type>(r);
}
template <class T>

Modified: trunk/libs/math/doc/sf_and_dist/error_handling.qbk
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/error_handling.qbk (original)
+++ trunk/libs/math/doc/sf_and_dist/error_handling.qbk 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -109,8 +109,10 @@
[table Possible Actions for Rounding Errors
[[Action] [Behaviour]]
[[throw_on_error][Throws `boost::math::rounding_error`]]
-[[errno_on_error][Sets `::errno` to `ERANGE` and returns an unspecified value.]]
-[[ignore_error][[*Returns the an unspecified value.]]]
+[[errno_on_error][Sets `::errno` to `ERANGE` and returns the largest representable value of the target integer type
+(or the most negative value if the argument to the function was less than zero).]]
+[[ignore_error][[*Returns the largest representable value of the target integer type
+(or the most negative value if the argument to the function was less than zero).]]]
[[user_error][Returns the result of `boost::math::policies::user_rounding_error`:
[link math_toolkit.policy.pol_tutorial.user_def_err_pol
this function must be defined by the user].]]

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -53,7 +53,7 @@
 Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and
 Thijs van den Berg</div>
<div><div class="legalnotice">
-<a name="id867111"></a>
+<a name="id973452"></a>
 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)
 
@@ -64,440 +64,445 @@
<div class="toc">
Table of Contents
<dl>
-<dt>Overview</dt>
+<dt> Overview</dt>
<dd><dl>
-<dt>About the Math Toolkit</dt>
-<dt>Navigation</dt>
-<dt><a href="math_toolkit/main_overview/directories.html">Directory and
+<dt> About the Math Toolkit</dt>
+<dt> Navigation</dt>
+<dt><a href="math_toolkit/main_overview/directories.html"> Directory and
 File Structure</a></dt>
-<dt>Namespaces</dt>
-<dt><a href="math_toolkit/main_overview/result_type.html">Calculation of
- the Type of the Result</a></dt>
-<dt>Error Handling</dt>
-<dt>Compilers</dt>
-<dt><a href="math_toolkit/main_overview/config_macros.html">Configuration
+<dt> Namespaces</dt>
+<dt><a href="math_toolkit/main_overview/result_type.html"> Calculation
+ of the Type of the Result</a></dt>
+<dt> Error Handling</dt>
+<dt> Compilers</dt>
+<dt><a href="math_toolkit/main_overview/config_macros.html"> Configuration
 Macros</a></dt>
-<dt>Policies</dt>
-<dt>Thread Safety</dt>
-<dt>Performance</dt>
-<dt><a href="math_toolkit/main_overview/building.html">If and How to Build
+<dt> Policies</dt>
+<dt> Thread Safety</dt>
+<dt> Performance</dt>
+<dt><a href="math_toolkit/main_overview/building.html"> If and How to Build
 a Boost.Math Library, and its Examples and Tests</a></dt>
-<dt><a href="math_toolkit/main_overview/history1.html">History and What's
+<dt><a href="math_toolkit/main_overview/history1.html"> History and What's
 New</a></dt>
-<dt><a href="math_toolkit/main_overview/tr1.html">C99 and C++ TR1 C-style
+<dt><a href="math_toolkit/main_overview/tr1.html"> C99 and C++ TR1 C-style
 Functions</a></dt>
-<dt><a href="math_toolkit/main_overview/faq.html">Frequently Asked Questions
+<dt><a href="math_toolkit/main_overview/faq.html"> Frequently Asked Questions
 FAQ</a></dt>
-<dt><a href="math_toolkit/main_overview/contact.html">Contact Info and
+<dt><a href="math_toolkit/main_overview/contact.html"> Contact Info and
 Support</a></dt>
</dl></dd>
-<dt>Statistical Distributions and Functions</dt>
+<dt> Statistical Distributions and Functions</dt>
<dd><dl>
-<dt><a href="math_toolkit/dist/stat_tut.html">Statistical Distributions
+<dt><a href="math_toolkit/dist/stat_tut.html"> Statistical Distributions
 Tutorial</a></dt>
<dd><dl>
-<dt>Overview of Distributions</dt>
+<dt> Overview of Distributions</dt>
<dd><dl>
-<dt><a href="math_toolkit/dist/stat_tut/overview/headers.html">Headers
+<dt><a href="math_toolkit/dist/stat_tut/overview/headers.html"> Headers
 and Namespaces</a></dt>
-<dt><a href="math_toolkit/dist/stat_tut/overview/objects.html">Distributions
+<dt><a href="math_toolkit/dist/stat_tut/overview/objects.html"> Distributions
 are Objects</a></dt>
-<dt><a href="math_toolkit/dist/stat_tut/overview/generic.html">Generic
+<dt><a href="math_toolkit/dist/stat_tut/overview/generic.html"> Generic
 operations common to all distributions are non-member functions</a></dt>
-<dt><a href="math_toolkit/dist/stat_tut/overview/complements.html">Complements
- are supported too - and when to use them</a></dt>
-<dt><a href="math_toolkit/dist/stat_tut/overview/parameters.html">Parameters
- can be calculated</a></dt>
-<dt>Summary</dt>
-</dl></dd>
-<dt>Worked Examples</dt>
-<dd><dl>
-<dt><a href="math_toolkit/dist/stat_tut/weg/dist_construct_eg.html">Distribution
- Construction Example</a></dt>
-<dt><a href="math_toolkit/dist/stat_tut/weg/st_eg.html">Student's t
+<dt><a href="math_toolkit/dist/stat_tut/overview/complements.html">
+ Complements are supported too - and when to use them</a></dt>
+<dt><a href="math_toolkit/dist/stat_tut/overview/parameters.html">
+ Parameters can be calculated</a></dt>
+<dt> Summary</dt>
+</dl></dd>
+<dt> Worked Examples</dt>
+<dd><dl>
+<dt><a href="math_toolkit/dist/stat_tut/weg/dist_construct_eg.html">
+ Distribution Construction Example</a></dt>
+<dt><a href="math_toolkit/dist/stat_tut/weg/st_eg.html"> Student's
+ t Distribution Examples</a></dt>
+<dt><a href="math_toolkit/dist/stat_tut/weg/cs_eg.html"> Chi Squared
 Distribution Examples</a></dt>
-<dt><a href="math_toolkit/dist/stat_tut/weg/cs_eg.html">Chi Squared
- Distribution Examples</a></dt>
-<dt><a href="math_toolkit/dist/stat_tut/weg/f_eg.html">F Distribution
+<dt><a href="math_toolkit/dist/stat_tut/weg/f_eg.html"> F Distribution
 Examples</a></dt>
-<dt><a href="math_toolkit/dist/stat_tut/weg/binom_eg.html">Binomial
+<dt><a href="math_toolkit/dist/stat_tut/weg/binom_eg.html"> Binomial
 Distribution Examples</a></dt>
-<dt><a href="math_toolkit/dist/stat_tut/weg/geometric_eg.html">Geometric
+<dt><a href="math_toolkit/dist/stat_tut/weg/geometric_eg.html"> Geometric
 Distribution Examples</a></dt>
-<dt><a href="math_toolkit/dist/stat_tut/weg/neg_binom_eg.html">Negative
+<dt><a href="math_toolkit/dist/stat_tut/weg/neg_binom_eg.html"> Negative
 Binomial Distribution Examples</a></dt>
-<dt><a href="math_toolkit/dist/stat_tut/weg/normal_example.html">Normal
+<dt><a href="math_toolkit/dist/stat_tut/weg/normal_example.html"> Normal
 Distribution Examples</a></dt>
-<dt><a href="math_toolkit/dist/stat_tut/weg/nccs_eg.html">Non Central
+<dt><a href="math_toolkit/dist/stat_tut/weg/nccs_eg.html"> Non Central
 Chi Squared Example</a></dt>
-<dt><a href="math_toolkit/dist/stat_tut/weg/error_eg.html">Error Handling
+<dt><a href="math_toolkit/dist/stat_tut/weg/error_eg.html"> Error Handling
 Example</a></dt>
-<dt><a href="math_toolkit/dist/stat_tut/weg/find_eg.html">Find Location
+<dt><a href="math_toolkit/dist/stat_tut/weg/find_eg.html"> Find Location
 and Scale Examples</a></dt>
-<dt><a href="math_toolkit/dist/stat_tut/weg/nag_library.html">Comparison
+<dt><a href="math_toolkit/dist/stat_tut/weg/nag_library.html"> Comparison
 with C, R, FORTRAN-style Free Functions</a></dt>
-<dt><a href="math_toolkit/dist/stat_tut/weg/c_sharp.html">Using the
+<dt><a href="math_toolkit/dist/stat_tut/weg/c_sharp.html"> Using the
 Distributions from Within C#</a></dt>
</dl></dd>
-<dt><a href="math_toolkit/dist/stat_tut/variates.html">Random Variates
+<dt><a href="math_toolkit/dist/stat_tut/variates.html"> Random Variates
 and Distribution Parameters</a></dt>
-<dt><a href="math_toolkit/dist/stat_tut/dist_params.html">Discrete Probability
+<dt><a href="math_toolkit/dist/stat_tut/dist_params.html"> Discrete Probability
 Distributions</a></dt>
</dl></dd>
-<dt><a href="math_toolkit/dist/dist_ref.html">Statistical Distributions
+<dt><a href="math_toolkit/dist/dist_ref.html"> Statistical Distributions
 Reference</a></dt>
<dd><dl>
-<dt>Non-Member Properties</dt>
-<dt>Distributions</dt>
+<dt> Non-Member Properties</dt>
+<dt> Distributions</dt>
<dd><dl>
-<dt><a href="math_toolkit/dist/dist_ref/dists/bernoulli_dist.html">Bernoulli
- Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/beta_dist.html">Beta
+<dt><a href="math_toolkit/dist/dist_ref/dists/bernoulli_dist.html">
+ Bernoulli Distribution</a></dt>
+<dt><a href="math_toolkit/dist/dist_ref/dists/beta_dist.html"> Beta
 Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/binomial_dist.html">Binomial
- Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/cauchy_dist.html">Cauchy-Lorentz
+<dt><a href="math_toolkit/dist/dist_ref/dists/binomial_dist.html">
+ Binomial Distribution</a></dt>
+<dt><a href="math_toolkit/dist/dist_ref/dists/cauchy_dist.html"> Cauchy-Lorentz
 Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/chi_squared_dist.html">Chi
- Squared Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/exp_dist.html">Exponential
+<dt><a href="math_toolkit/dist/dist_ref/dists/chi_squared_dist.html">
+ Chi Squared Distribution</a></dt>
+<dt><a href="math_toolkit/dist/dist_ref/dists/exp_dist.html"> Exponential
 Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/extreme_dist.html">Extreme
+<dt><a href="math_toolkit/dist/dist_ref/dists/extreme_dist.html"> Extreme
 Value Distribution</a></dt>
-<dt>F Distribution</dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/gamma_dist.html">Gamma
+<dt> F Distribution</dt>
+<dt><a href="math_toolkit/dist/dist_ref/dists/gamma_dist.html"> Gamma
 (and Erlang) Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/geometric_dist.html">Geometric
- Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html">Hypergeometric
- Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html">Inverse
- Chi Squared Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html">Inverse
- Gamma Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html">Inverse
- Gaussian (or Inverse Normal) Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/laplace_dist.html">Laplace
- Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/logistic_dist.html">Logistic
- Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/lognormal_dist.html">Log
- Normal Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html">Negative
- Binomial Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/nc_beta_dist.html">Noncentral
+<dt><a href="math_toolkit/dist/dist_ref/dists/geometric_dist.html">
+ Geometric Distribution</a></dt>
+<dt><a href="math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html">
+ Hypergeometric Distribution</a></dt>
+<dt><a href="math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html">
+ Inverse Chi Squared Distribution</a></dt>
+<dt><a href="math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html">
+ Inverse Gamma Distribution</a></dt>
+<dt><a href="math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html">
+ Inverse Gaussian (or Inverse Normal) Distribution</a></dt>
+<dt><a href="math_toolkit/dist/dist_ref/dists/laplace_dist.html"> Laplace
+ Distribution</a></dt>
+<dt><a href="math_toolkit/dist/dist_ref/dists/logistic_dist.html">
+ Logistic Distribution</a></dt>
+<dt><a href="math_toolkit/dist/dist_ref/dists/lognormal_dist.html">
+ Log Normal Distribution</a></dt>
+<dt><a href="math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html">
+ Negative Binomial Distribution</a></dt>
+<dt><a href="math_toolkit/dist/dist_ref/dists/nc_beta_dist.html"> Noncentral
 Beta Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html">Noncentral
- Chi-Squared Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/nc_f_dist.html">Noncentral
+<dt><a href="math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html">
+ Noncentral Chi-Squared Distribution</a></dt>
+<dt><a href="math_toolkit/dist/dist_ref/dists/nc_f_dist.html"> Noncentral
 F Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/nc_t_dist.html">Noncentral
+<dt><a href="math_toolkit/dist/dist_ref/dists/nc_t_dist.html"> Noncentral
 T Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/normal_dist.html">Normal
+<dt><a href="math_toolkit/dist/dist_ref/dists/normal_dist.html"> Normal
 (Gaussian) Distribution</a></dt>
-<dt>Pareto Distribution</dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/poisson_dist.html">Poisson
+<dt><a href="math_toolkit/dist/dist_ref/dists/pareto.html"> Pareto
 Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/rayleigh.html">Rayleigh
+<dt><a href="math_toolkit/dist/dist_ref/dists/poisson_dist.html"> Poisson
 Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/students_t_dist.html">Students
- t Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/triangular_dist.html">Triangular
+<dt><a href="math_toolkit/dist/dist_ref/dists/rayleigh.html"> Rayleigh
 Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/uniform_dist.html">Uniform
+<dt><a href="math_toolkit/dist/dist_ref/dists/students_t_dist.html">
+ Students t Distribution</a></dt>
+<dt><a href="math_toolkit/dist/dist_ref/dists/triangular_dist.html">
+ Triangular Distribution</a></dt>
+<dt><a href="math_toolkit/dist/dist_ref/dists/uniform_dist.html"> Uniform
 Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/weibull_dist.html">Weibull
+<dt><a href="math_toolkit/dist/dist_ref/dists/weibull_dist.html"> Weibull
 Distribution</a></dt>
</dl></dd>
-<dt><a href="math_toolkit/dist/dist_ref/dist_algorithms.html">Distribution
+<dt><a href="math_toolkit/dist/dist_ref/dist_algorithms.html"> Distribution
 Algorithms</a></dt>
</dl></dd>
-<dt>Extras/Future Directions</dt>
+<dt> Extras/Future Directions</dt>
</dl></dd>
-<dt>Special Functions</dt>
+<dt> Special Functions</dt>
<dd><dl>
-<dt>Gamma Functions</dt>
+<dt> Gamma Functions</dt>
<dd><dl>
-<dt>Gamma</dt>
-<dt>Log Gamma</dt>
-<dt>Digamma</dt>
-<dt><a href="math_toolkit/special/sf_gamma/gamma_ratios.html">Ratios
+<dt> Gamma</dt>
+<dt> Log Gamma</dt>
+<dt> Digamma</dt>
+<dt><a href="math_toolkit/special/sf_gamma/gamma_ratios.html"> Ratios
 of Gamma Functions</a></dt>
-<dt><a href="math_toolkit/special/sf_gamma/igamma.html">Incomplete Gamma
+<dt><a href="math_toolkit/special/sf_gamma/igamma.html"> Incomplete Gamma
 Functions</a></dt>
-<dt><a href="math_toolkit/special/sf_gamma/igamma_inv.html">Incomplete
+<dt><a href="math_toolkit/special/sf_gamma/igamma_inv.html"> Incomplete
 Gamma Function Inverses</a></dt>
-<dt><a href="math_toolkit/special/sf_gamma/gamma_derivatives.html">Derivative
+<dt><a href="math_toolkit/special/sf_gamma/gamma_derivatives.html"> Derivative
 of the Incomplete Gamma Function</a></dt>
</dl></dd>
-<dt><a href="math_toolkit/special/factorials.html">Factorials and Binomial
+<dt><a href="math_toolkit/special/factorials.html"> Factorials and Binomial
 Coefficients</a></dt>
<dd><dl>
-<dt>Factorial</dt>
-<dt><a href="math_toolkit/special/factorials/sf_double_factorial.html">Double
- Factorial</a></dt>
-<dt><a href="math_toolkit/special/factorials/sf_rising_factorial.html">Rising
- Factorial</a></dt>
-<dt><a href="math_toolkit/special/factorials/sf_falling_factorial.html">Falling
- Factorial</a></dt>
-<dt><a href="math_toolkit/special/factorials/sf_binomial.html">Binomial
+<dt> Factorial</dt>
+<dt><a href="math_toolkit/special/factorials/sf_double_factorial.html">
+ Double Factorial</a></dt>
+<dt><a href="math_toolkit/special/factorials/sf_rising_factorial.html">
+ Rising Factorial</a></dt>
+<dt><a href="math_toolkit/special/factorials/sf_falling_factorial.html">
+ Falling Factorial</a></dt>
+<dt><a href="math_toolkit/special/factorials/sf_binomial.html"> Binomial
 Coefficients</a></dt>
</dl></dd>
-<dt>Beta Functions</dt>
+<dt> Beta Functions</dt>
<dd><dl>
-<dt>Beta</dt>
-<dt><a href="math_toolkit/special/sf_beta/ibeta_function.html">Incomplete
+<dt> Beta</dt>
+<dt><a href="math_toolkit/special/sf_beta/ibeta_function.html"> Incomplete
 Beta Functions</a></dt>
-<dt><a href="math_toolkit/special/sf_beta/ibeta_inv_function.html">The
+<dt><a href="math_toolkit/special/sf_beta/ibeta_inv_function.html"> The
 Incomplete Beta Function Inverses</a></dt>
-<dt><a href="math_toolkit/special/sf_beta/beta_derivative.html">Derivative
+<dt><a href="math_toolkit/special/sf_beta/beta_derivative.html"> Derivative
 of the Incomplete Beta Function</a></dt>
</dl></dd>
-<dt>Error Functions</dt>
+<dt> Error Functions</dt>
<dd><dl>
-<dt>Error Functions</dt>
-<dt><a href="math_toolkit/special/sf_erf/error_inv.html">Error Function
+<dt><a href="math_toolkit/special/sf_erf/error_function.html"> Error
+ Functions</a></dt>
+<dt><a href="math_toolkit/special/sf_erf/error_inv.html"> Error Function
 Inverses</a></dt>
</dl></dd>
-<dt>Polynomials</dt>
+<dt> Polynomials</dt>
<dd><dl>
-<dt><a href="math_toolkit/special/sf_poly/legendre.html">Legendre (and
+<dt><a href="math_toolkit/special/sf_poly/legendre.html"> Legendre (and
 Associated) Polynomials</a></dt>
-<dt><a href="math_toolkit/special/sf_poly/laguerre.html">Laguerre (and
+<dt><a href="math_toolkit/special/sf_poly/laguerre.html"> Laguerre (and
 Associated) Polynomials</a></dt>
-<dt>Hermite Polynomials</dt>
-<dt>Spherical Harmonics</dt>
+<dt> Hermite Polynomials</dt>
+<dt> Spherical Harmonics</dt>
</dl></dd>
-<dt>Bessel Functions</dt>
+<dt> Bessel Functions</dt>
<dd><dl>
-<dt><a href="math_toolkit/special/bessel/bessel_over.html">Bessel Function
+<dt><a href="math_toolkit/special/bessel/bessel_over.html"> Bessel Function
 Overview</a></dt>
-<dt><a href="math_toolkit/special/bessel/bessel.html">Bessel Functions
+<dt><a href="math_toolkit/special/bessel/bessel.html"> Bessel Functions
 of the First and Second Kinds</a></dt>
-<dt><a href="math_toolkit/special/bessel/mbessel.html">Modified Bessel
- Functions of the First and Second Kinds</a></dt>
-<dt><a href="math_toolkit/special/bessel/sph_bessel.html">Spherical Bessel
+<dt><a href="math_toolkit/special/bessel/mbessel.html"> Modified Bessel
 Functions of the First and Second Kinds</a></dt>
+<dt><a href="math_toolkit/special/bessel/sph_bessel.html"> Spherical
+ Bessel Functions of the First and Second Kinds</a></dt>
</dl></dd>
-<dt>Elliptic Integrals</dt>
+<dt> Elliptic Integrals</dt>
<dd><dl>
-<dt><a href="math_toolkit/special/ellint/ellint_intro.html">Elliptic
+<dt><a href="math_toolkit/special/ellint/ellint_intro.html"> Elliptic
 Integral Overview</a></dt>
-<dt><a href="math_toolkit/special/ellint/ellint_carlson.html">Elliptic
+<dt><a href="math_toolkit/special/ellint/ellint_carlson.html"> Elliptic
 Integrals - Carlson Form</a></dt>
-<dt><a href="math_toolkit/special/ellint/ellint_1.html">Elliptic Integrals
+<dt><a href="math_toolkit/special/ellint/ellint_1.html"> Elliptic Integrals
 of the First Kind - Legendre Form</a></dt>
-<dt><a href="math_toolkit/special/ellint/ellint_2.html">Elliptic Integrals
+<dt><a href="math_toolkit/special/ellint/ellint_2.html"> Elliptic Integrals
 of the Second Kind - Legendre Form</a></dt>
-<dt><a href="math_toolkit/special/ellint/ellint_3.html">Elliptic Integrals
+<dt><a href="math_toolkit/special/ellint/ellint_3.html"> Elliptic Integrals
 of the Third Kind - Legendre Form</a></dt>
</dl></dd>
-<dt>Zeta Functions</dt>
-<dd><dl><dt>Riemann Zeta Function</dt></dl></dd>
-<dt>Exponential Integrals</dt>
-<dd><dl>
-<dt><a href="math_toolkit/special/expint/expint_n.html">Exponential Integral
- En</a></dt>
-<dt><a href="math_toolkit/special/expint/expint_i.html">Exponential Integral
- Ei</a></dt>
+<dt> Zeta Functions</dt>
+<dd><dl><dt> Riemann Zeta Function</dt></dl></dd>
+<dt> Exponential Integrals</dt>
+<dd><dl>
+<dt><a href="math_toolkit/special/expint/expint_n.html"> Exponential
+ Integral En</a></dt>
+<dt><a href="math_toolkit/special/expint/expint_i.html"> Exponential
+ Integral Ei</a></dt>
</dl></dd>
-<dt><a href="math_toolkit/special/powers.html">Logs, Powers, Roots and
+<dt><a href="math_toolkit/special/powers.html"> Logs, Powers, Roots and
 Exponentials</a></dt>
<dd><dl>
-<dt>log1p</dt>
-<dt>expm1</dt>
-<dt>cbrt</dt>
-<dt>sqrt1pm1</dt>
-<dt>powm1</dt>
-<dt>hypot</dt>
-<dt><a href="math_toolkit/special/powers/ct_pow.html">Compile Time Power
+<dt> log1p</dt>
+<dt> expm1</dt>
+<dt> cbrt</dt>
+<dt> sqrt1pm1</dt>
+<dt> powm1</dt>
+<dt> hypot</dt>
+<dt><a href="math_toolkit/special/powers/ct_pow.html"> Compile Time Power
 of a Runtime Base</a></dt>
</dl></dd>
-<dt><a href="math_toolkit/special/sinc.html">Sinus Cardinal and Hyperbolic
+<dt><a href="math_toolkit/special/sinc.html"> Sinus Cardinal and Hyperbolic
 Sinus Cardinal Functions</a></dt>
<dd><dl>
-<dt><a href="math_toolkit/special/sinc/sinc_overview.html">Sinus Cardinal
+<dt><a href="math_toolkit/special/sinc/sinc_overview.html"> Sinus Cardinal
 and Hyperbolic Sinus Cardinal Functions Overview</a></dt>
<dt>sinc_pi</dt>
<dt>sinhc_pi</dt>
</dl></dd>
-<dt>Inverse Hyperbolic Functions</dt>
+<dt> Inverse Hyperbolic Functions</dt>
<dd><dl>
-<dt><a href="math_toolkit/special/inv_hyper/inv_hyper_over.html">Inverse
+<dt><a href="math_toolkit/special/inv_hyper/inv_hyper_over.html"> Inverse
 Hyperbolic Functions Overview</a></dt>
-<dt>acosh</dt>
-<dt>asinh</dt>
-<dt>atanh</dt>
+<dt> acosh</dt>
+<dt> asinh</dt>
+<dt> atanh</dt>
</dl></dd>
</dl></dd>
-<dt>Floating Point Utilities</dt>
+<dt> Floating Point Utilities</dt>
<dd><dl>
-<dt><a href="math_toolkit/utils/rounding.html">Rounding Truncation and
+<dt><a href="math_toolkit/utils/rounding.html"> Rounding Truncation and
 Integer Conversion</a></dt>
<dd><dl>
-<dt>Rounding Functions</dt>
-<dt>Truncation Functions</dt>
-<dt><a href="math_toolkit/utils/rounding/modf.html">Integer and Fractional
+<dt> Rounding Functions</dt>
+<dt> Truncation Functions</dt>
+<dt><a href="math_toolkit/utils/rounding/modf.html"> Integer and Fractional
 Part Splitting (modf)</a></dt>
</dl></dd>
-<dt><a href="math_toolkit/utils/fpclass.html">Floating-Point Classification:
+<dt><a href="math_toolkit/utils/fpclass.html"> Floating-Point Classification:
 Infinities and NaN's</a></dt>
-<dt><a href="math_toolkit/utils/sign_functions.html">Sign Manipulation
+<dt><a href="math_toolkit/utils/sign_functions.html"> Sign Manipulation
 Functions</a></dt>
-<dt><a href="math_toolkit/utils/next_float.html">Floating-Point Representation
+<dt><a href="math_toolkit/utils/next_float.html"> Floating-Point Representation
 Distance (ULP), and Finding Adjacent Floating-Point Values</a></dt>
<dd><dl>
-<dt><a href="math_toolkit/utils/next_float/nextafter.html">Finding the
+<dt><a href="math_toolkit/utils/next_float/nextafter.html"> Finding the
 Next Representable Value in a Specific Direction (nextafter)</a></dt>
-<dt><a href="math_toolkit/utils/next_float/float_next.html">Finding the
- Next Greater Representable Value (float_next)</a></dt>
-<dt><a href="math_toolkit/utils/next_float/float_prior.html">Finding
+<dt><a href="math_toolkit/utils/next_float/float_next.html"> Finding
+ the Next Greater Representable Value (float_next)</a></dt>
+<dt><a href="math_toolkit/utils/next_float/float_prior.html"> Finding
 the Next Smaller Representable Value (float_prior)</a></dt>
-<dt><a href="math_toolkit/utils/next_float/float_distance.html">Calculating
+<dt><a href="math_toolkit/utils/next_float/float_distance.html"> Calculating
 the Representation Distance Between Two Floating Point Values (ULP) float_distance</a></dt>
-<dt><a href="math_toolkit/utils/next_float/float_advance.html">Advancing
+<dt><a href="math_toolkit/utils/next_float/float_advance.html"> Advancing
 a Floating Point Value by a Specific Representation Distance (ULP) float_advance</a></dt>
</dl></dd>
</dl></dd>
-<dt><a href="math_toolkit/extern_c.html">TR1 and C99 external "C"
+<dt><a href="math_toolkit/extern_c.html"> TR1 and C99 external "C"
 Functions</a></dt>
<dd><dl>
-<dt>C99 and TR1 C Functions Overview</dt>
-<dt>C99 C Functions</dt>
-<dt><a href="math_toolkit/extern_c/tr1_ref.html">TR1 C Functions Quick
+<dt> C99 and TR1 C Functions Overview</dt>
+<dt> C99 C Functions</dt>
+<dt><a href="math_toolkit/extern_c/tr1_ref.html"> TR1 C Functions Quick
 Reference</a></dt>
</dl></dd>
-<dt>Tools, Constants and Internal Details</dt>
+<dt> Tools, Constants and Internal Details</dt>
<dd><dl>
-<dt>Overview</dt>
-<dt><a href="math_toolkit/toolkit/internals1.html">Utilities - Constants
+<dt> Overview</dt>
+<dt><a href="math_toolkit/toolkit/internals1.html"> Utilities - Constants
 & Tools</a></dt>
<dd><dl>
-<dt><a href="math_toolkit/toolkit/internals1/constants.html">Numeric
+<dt><a href="math_toolkit/toolkit/internals1/constants.html"> Numeric
 Constants</a></dt>
-<dt><a href="math_toolkit/toolkit/internals1/series_evaluation.html">Series
- Evaluation</a></dt>
-<dt><a href="math_toolkit/toolkit/internals1/cf.html">Continued Fraction
+<dt><a href="math_toolkit/toolkit/internals1/series_evaluation.html">
+ Series Evaluation</a></dt>
+<dt><a href="math_toolkit/toolkit/internals1/cf.html"> Continued Fraction
 Evaluation</a></dt>
-<dt><a href="math_toolkit/toolkit/internals1/rational.html">Polynomial
+<dt><a href="math_toolkit/toolkit/internals1/rational.html"> Polynomial
 and Rational Function Evaluation</a></dt>
-<dt><a href="math_toolkit/toolkit/internals1/roots.html">Root Finding
+<dt><a href="math_toolkit/toolkit/internals1/roots.html"> Root Finding
 With Derivatives: Newton-Raphson, Halley & Schroeder</a></dt>
-<dt><a href="math_toolkit/toolkit/internals1/roots2.html">Root Finding
+<dt><a href="math_toolkit/toolkit/internals1/roots2.html"> Root Finding
 Without Derivatives: Bisection, Bracket and TOMS748</a></dt>
-<dt><a href="math_toolkit/toolkit/internals1/minima.html">Locating Function
+<dt><a href="math_toolkit/toolkit/internals1/minima.html"> Locating Function
 Minima: Brent's algorithm</a></dt>
-<dt>Tuples</dt>
+<dt> Tuples</dt>
</dl></dd>
-<dt>Testing and Development</dt>
+<dt> Testing and Development</dt>
<dd><dl>
-<dt>Polynomials</dt>
-<dt><a href="math_toolkit/toolkit/internals2/minimax.html">Minimax Approximations
+<dt> Polynomials</dt>
+<dt><a href="math_toolkit/toolkit/internals2/minimax.html"> Minimax Approximations
 and the Remez Algorithm</a></dt>
-<dt><a href="math_toolkit/toolkit/internals2/error_test.html">Relative
+<dt><a href="math_toolkit/toolkit/internals2/error_test.html"> Relative
 Error and Testing</a></dt>
-<dt><a href="math_toolkit/toolkit/internals2/test_data.html">Graphing,
+<dt><a href="math_toolkit/toolkit/internals2/test_data.html"> Graphing,
 Profiling, and Generating Test Data for Special Functions</a></dt>
</dl></dd>
</dl></dd>
-<dt><a href="math_toolkit/using_udt.html">Use with User-Defined Floating-Point
+<dt><a href="math_toolkit/using_udt.html"> Use with User-Defined Floating-Point
 Types</a></dt>
<dd><dl>
-<dt><a href="math_toolkit/using_udt/use_ntl.html">Using With NTL - a High-Precision
+<dt><a href="math_toolkit/using_udt/use_ntl.html"> Using With NTL - a High-Precision
 Floating-Point Library</a></dt>
-<dt><a href="math_toolkit/using_udt/use_mpfr.html">Using With MPFR / GMP
+<dt><a href="math_toolkit/using_udt/use_mpfr.html"> Using With MPFR / GMP
 - a High-Precision Floating-Point Library</a></dt>
-<dt><a href="math_toolkit/using_udt/concepts.html">Conceptual Requirements
+<dt><a href="math_toolkit/using_udt/concepts.html"> Conceptual Requirements
 for Real Number Types</a></dt>
-<dt><a href="math_toolkit/using_udt/dist_concept.html">Conceptual Requirements
+<dt><a href="math_toolkit/using_udt/dist_concept.html"> Conceptual Requirements
 for Distribution Types</a></dt>
-<dt><a href="math_toolkit/using_udt/archetypes.html">Conceptual Archetypes
+<dt><a href="math_toolkit/using_udt/archetypes.html"> Conceptual Archetypes
 for Reals and Distributions</a></dt>
</dl></dd>
-<dt>Policies</dt>
+<dt> Policies</dt>
<dd><dl>
-<dt>Policy Overview</dt>
-<dt>Policy Tutorial</dt>
+<dt> Policy Overview</dt>
+<dt> Policy Tutorial</dt>
<dd><dl>
-<dt><a href="math_toolkit/policy/pol_tutorial/what_is_a_policy.html">So
- Just What is a Policy Anyway?</a></dt>
-<dt><a href="math_toolkit/policy/pol_tutorial/policy_tut_defaults.html">Policies
- Have Sensible Defaults</a></dt>
-<dt><a href="math_toolkit/policy/pol_tutorial/policy_usage.html">So How
- are Policies Used Anyway?</a></dt>
-<dt><a href="math_toolkit/policy/pol_tutorial/changing_policy_defaults.html">Changing
- the Policy Defaults</a></dt>
-<dt><a href="math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html">Setting
- Policies for Distributions on an Ad Hoc Basis</a></dt>
-<dt><a href="math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html">Changing
- the Policy on an Ad Hoc Basis for the Special Functions</a></dt>
-<dt><a href="math_toolkit/policy/pol_tutorial/namespace_policies.html">Setting
- Policies at Namespace or Translation Unit Scope</a></dt>
-<dt><a href="math_toolkit/policy/pol_tutorial/user_def_err_pol.html">Calling
- User Defined Error Handlers</a></dt>
-<dt><a href="math_toolkit/policy/pol_tutorial/understand_dis_quant.html">Understanding
- Quantiles of Discrete Distributions</a></dt>
-</dl></dd>
-<dt>Policy Reference</dt>
-<dd><dl>
-<dt><a href="math_toolkit/policy/pol_ref/error_handling_policies.html">Error
- Handling Policies</a></dt>
-<dt><a href="math_toolkit/policy/pol_ref/internal_promotion.html">Internal
+<dt><a href="math_toolkit/policy/pol_tutorial/what_is_a_policy.html">
+ So Just What is a Policy Anyway?</a></dt>
+<dt><a href="math_toolkit/policy/pol_tutorial/policy_tut_defaults.html">
+ Policies Have Sensible Defaults</a></dt>
+<dt><a href="math_toolkit/policy/pol_tutorial/policy_usage.html"> So
+ How are Policies Used Anyway?</a></dt>
+<dt><a href="math_toolkit/policy/pol_tutorial/changing_policy_defaults.html">
+ Changing the Policy Defaults</a></dt>
+<dt><a href="math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html">
+ Setting Policies for Distributions on an Ad Hoc Basis</a></dt>
+<dt><a href="math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html">
+ Changing the Policy on an Ad Hoc Basis for the Special Functions</a></dt>
+<dt><a href="math_toolkit/policy/pol_tutorial/namespace_policies.html">
+ Setting Policies at Namespace or Translation Unit Scope</a></dt>
+<dt><a href="math_toolkit/policy/pol_tutorial/user_def_err_pol.html">
+ Calling User Defined Error Handlers</a></dt>
+<dt><a href="math_toolkit/policy/pol_tutorial/understand_dis_quant.html">
+ Understanding Quantiles of Discrete Distributions</a></dt>
+</dl></dd>
+<dt> Policy Reference</dt>
+<dd><dl>
+<dt><a href="math_toolkit/policy/pol_ref/error_handling_policies.html">
+ Error Handling Policies</a></dt>
+<dt><a href="math_toolkit/policy/pol_ref/internal_promotion.html"> Internal
 Floating-point Promotion Policies</a></dt>
-<dt><a href="math_toolkit/policy/pol_ref/assert_undefined.html">Mathematically
+<dt><a href="math_toolkit/policy/pol_ref/assert_undefined.html"> Mathematically
 Undefined Function Policies</a></dt>
-<dt><a href="math_toolkit/policy/pol_ref/discrete_quant_ref.html">Discrete
+<dt><a href="math_toolkit/policy/pol_ref/discrete_quant_ref.html"> Discrete
 Quantile Policies</a></dt>
-<dt><a href="math_toolkit/policy/pol_ref/precision_pol.html">Precision
+<dt><a href="math_toolkit/policy/pol_ref/precision_pol.html"> Precision
 Policies</a></dt>
-<dt><a href="math_toolkit/policy/pol_ref/iteration_pol.html">Iteration
+<dt><a href="math_toolkit/policy/pol_ref/iteration_pol.html"> Iteration
 Limits Policies</a></dt>
-<dt><a href="math_toolkit/policy/pol_ref/policy_defaults.html">Using
+<dt><a href="math_toolkit/policy/pol_ref/policy_defaults.html"> Using
 Macros to Change the Policy Defaults</a></dt>
-<dt><a href="math_toolkit/policy/pol_ref/namespace_pol.html">Setting
+<dt><a href="math_toolkit/policy/pol_ref/namespace_pol.html"> Setting
 Polices at Namespace Scope</a></dt>
-<dt><a href="math_toolkit/policy/pol_ref/pol_ref_ref.html">Policy Class
+<dt><a href="math_toolkit/policy/pol_ref/pol_ref_ref.html"> Policy Class
 Reference</a></dt>
</dl></dd>
</dl></dd>
-<dt>Performance</dt>
+<dt> Performance</dt>
<dd><dl>
-<dt>Performance Overview</dt>
-<dt>Interpreting these Results</dt>
-<dt><a href="math_toolkit/perf/getting_best.html">Getting the Best Performance
+<dt> Performance Overview</dt>
+<dt> Interpreting these Results</dt>
+<dt><a href="math_toolkit/perf/getting_best.html"> Getting the Best Performance
 from this Library</a></dt>
-<dt>Comparing Compilers</dt>
-<dt>Performance Tuning Macros</dt>
-<dt><a href="math_toolkit/perf/comparisons.html">Comparisons to Other Open
- Source Libraries</a></dt>
-<dt><a href="math_toolkit/perf/perf_test_app.html">The Performance Test
+<dt> Comparing Compilers</dt>
+<dt> Performance Tuning Macros</dt>
+<dt><a href="math_toolkit/perf/comparisons.html"> Comparisons to Other
+ Open Source Libraries</a></dt>
+<dt><a href="math_toolkit/perf/perf_test_app.html"> The Performance Test
 Application</a></dt>
</dl></dd>
-<dt>Backgrounders</dt>
+<dt> Backgrounders</dt>
<dd><dl>
-<dt><a href="math_toolkit/backgrounders/implementation.html">Additional
+<dt><a href="math_toolkit/backgrounders/implementation.html"> Additional
 Implementation Notes</a></dt>
-<dt>Relative Error</dt>
-<dt>The Lanczos Approximation</dt>
-<dt>The Remez Method</dt>
-<dt>References</dt>
-</dl></dd>
-<dt>Library Status</dt>
-<dd><dl>
-<dt>History and What's New</dt>
-<dt>Known Issues, and TODO List</dt>
-<dt>Credits and Acknowledgements</dt>
+<dt><a href="math_toolkit/backgrounders/relative_error.html"> Relative
+ Error</a></dt>
+<dt> The Lanczos Approximation</dt>
+<dt> The Remez Method</dt>
+<dt> References</dt>
+</dl></dd>
+<dt> Library Status</dt>
+<dd><dl>
+<dt> History and What's New</dt>
+<dt> Known Issues, and TODO List</dt>
+<dt> Credits and Acknowledgements</dt>
</dl></dd>
</dl>
</div>

+ 
+
 This manual is also available in <a href="http://svn.boost.org/svn/boost/sandbox/pdf/math/release/math.pdf" target="_top">printer
 friendly PDF format</a>, and as a CD ISBN 0-9504833-2-X 978-0-9504833-2-0,
 Classification 519.2-dc22.
 
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
-<td align="left">Last revised: December 14, 2010 at 16:47:10 GMT</td>
+<td align="left">Last revised: December 14, 2010 at 19:14:57 GMT</td>
<td align="right"><div class="copyright-footer"></div></td>
</tr></table>
<hr>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,15 +24,16 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
-<a name="math_toolkit.backgrounders"></a><a class="link" href="backgrounders.html" title="Backgrounders">Backgrounders</a>
+<a name="math_toolkit.backgrounders"></a><a class="link" href="backgrounders.html" title="Backgrounders"> Backgrounders</a>
</h2></div></div></div>
<div class="toc"><dl>
-<dt><a href="backgrounders/implementation.html">Additional
+<dt><a href="backgrounders/implementation.html"> Additional
Implementation Notes</a></dt>
-<dt>Relative Error</dt>
-<dt>The Lanczos Approximation</dt>
-<dt>The Remez Method</dt>
-<dt>References</dt>
+<dt><a href="backgrounders/relative_error.html"> Relative
+ Error</a></dt>
+<dt> The Lanczos Approximation</dt>
+<dt> The Remez Method</dt>
+<dt> References</dt>
</dl></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h3 class="title">
-<a name="math_toolkit.backgrounders.implementation"></a><a class="link" href="implementation.html" title="Additional Implementation Notes">Additional
+<a name="math_toolkit.backgrounders.implementation"></a><a class="link" href="implementation.html" title="Additional Implementation Notes"> Additional
 Implementation Notes</a>
</h3></div></div></div>

@@ -33,7 +33,7 @@
 and reflect more the general implementation philosophy used.
 
<a name="math_toolkit.backgrounders.implementation.implemention_philosophy"></a><h5>
-<a name="id1273460"></a>
+<a name="id1379887"></a>
 <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.implemention_philosophy">Implemention
 philosophy</a>
 </h5>
@@ -85,7 +85,7 @@
 These could still provide sufficient accuracy for some speed-critical applications.
 
<a name="math_toolkit.backgrounders.implementation.accuracy_and_representation_of_test_values"></a><h5>
-<a name="id1273523"></a>
+<a name="id1379951"></a>
 <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.accuracy_and_representation_of_test_values">Accuracy
 and Representation of Test Values</a>
 </h5>
@@ -130,7 +130,7 @@
 binary value).
 
<a name="math_toolkit.backgrounders.implementation.tolerance_of_tests"></a><h5>
-<a name="id1273667"></a>
+<a name="id1380128"></a>
 <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.tolerance_of_tests">Tolerance
 of Tests</a>
 </h5>
@@ -156,7 +156,7 @@
 first that the suffix L is present, and then that the tolerance is big enough.
 
<a name="math_toolkit.backgrounders.implementation.handling_unsuitable_arguments"></a><h5>
-<a name="id1273712"></a>
+<a name="id1380172"></a>
 <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.handling_unsuitable_arguments">Handling
 Unsuitable Arguments</a>
 </h5>
@@ -224,7 +224,7 @@
 </td></tr>
</table></div>
<a name="math_toolkit.backgrounders.implementation.handling_of_functions_that_are_not_mathematically_defined"></a><h5>
-<a name="id1273841"></a>
+<a name="id1380302"></a>
 <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>
@@ -258,7 +258,7 @@
 </td></tr>
</table></div>
<a name="math_toolkit.backgrounders.implementation.median_of_distributions"></a><h5>
-<a name="id1273927"></a>
+<a name="id1380387"></a>
 <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.median_of_distributions">Median
 of distributions</a>
 </h5>
@@ -293,7 +293,7 @@
 Basic Statistics.</a> give more detail, in particular for discrete distributions.
 
<a name="math_toolkit.backgrounders.implementation.handling_of_floating_point_infinity"></a><h5>
-<a name="id1274045"></a>
+<a name="id1380506"></a>
 <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.handling_of_floating_point_infinity">Handling
 of Floating-Point Infinity</a>
 </h5>
@@ -337,7 +337,7 @@
 handling policies</a>.
 
<a name="math_toolkit.backgrounders.implementation.scale__shape_and_location"></a><h5>
-<a name="id1274132"></a>
+<a name="id1380592"></a>
 <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.scale__shape_and_location">Scale,
 Shape and Location</a>
 </h5>
@@ -364,7 +364,7 @@
 functions, they can be added if required.
 
<a name="math_toolkit.backgrounders.implementation.notes_on_implementation_of_specific_functions__amp__distributions"></a><h5>
-<a name="id1274467"></a>
+<a name="id1380927"></a>
 <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>
@@ -376,7 +376,7 @@
 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="id1274491"></a>
+<a name="id1380951"></a>
 <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.rational_approximations_used">Rational
 Approximations Used</a>
 </h5>
@@ -419,7 +419,7 @@
 to the "true" minimax solution.
 
<a name="math_toolkit.backgrounders.implementation.representation_of_mathematical_constants"></a><h5>
-<a name="id1274535"></a>
+<a name="id1380996"></a>
 <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.representation_of_mathematical_constants">Representation
 of Mathematical Constants</a>
 </h5>
@@ -480,7 +480,7 @@
double p = boost::math::constants::pi(); // Context does not allow for disambiguation of overloaded function
</pre>
<a name="math_toolkit.backgrounders.implementation.thread_safety"></a><h5>
-<a name="id1274921"></a>
+<a name="id1381382"></a>
 <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.thread_safety">Thread
 safety</a>
 </h5>
@@ -505,7 +505,7 @@
 the right thing here at some point.
 
<a name="math_toolkit.backgrounders.implementation.sources_of_test_data"></a><h5>
-<a name="id1274957"></a>
+<a name="id1381418"></a>
 <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.sources_of_test_data">Sources
 of Test Data</a>
 </h5>
@@ -546,7 +546,7 @@
 the underlying special function is known to be difficult to implement.
 
<a name="math_toolkit.backgrounders.implementation.creating_and_managing_the_equations"></a><h5>
-<a name="id1275026"></a>
+<a name="id1381486"></a>
 <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.creating_and_managing_the_equations">Creating
 and Managing the Equations</a>
 </h5>
@@ -648,8 +648,8 @@
<pre class="programlisting">
</pre>

- is provided in the xep.xml downloaded, but the Windows TrueType fonts are
- commented out.
+  is provided
+ in the xep.xml downloaded, but the Windows TrueType fonts are commented out.
 

 JM's XEP config file \xep\xep.xml has the following font configuration section
@@ -731,7 +731,7 @@
 HTML: this needs further investigation.
 
<a name="math_toolkit.backgrounders.implementation.producing_graphs"></a><h5>
-<a name="id1277263"></a>
+<a name="id1381743"></a>
 <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.producing_graphs">Producing
 Graphs</a>
 </h5>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,10 +24,10 @@
</div>
<div class="section" lang="en">
<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>
+<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="id1277592"></a>
+<a name="id1382076"></a>
 <a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.motivation">Motivation</a>
 </h5>

@@ -99,7 +99,7 @@
 functions divided by large powers into single (simpler) expressions.
 
<a name="math_toolkit.backgrounders.lanczos.the_approximation"></a><h5>
-<a name="id1277850"></a>
+<a name="id1383616"></a>
 <a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.the_approximation">The
 Approximation</a>
 </h5>
@@ -161,7 +161,7 @@
 </td></tr>
</table></div>
<a name="math_toolkit.backgrounders.lanczos.computing_the_coefficients"></a><h5>
-<a name="id1278042"></a>
+<a name="id1383808"></a>
 <a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.computing_the_coefficients">Computing
 the Coefficients</a>
 </h5>
@@ -205,7 +205,7 @@
 multiplied by F as the last step.
 
<a name="math_toolkit.backgrounders.lanczos.choosing_the_right_parameters"></a><h5>
-<a name="id1278199"></a>
+<a name="id1383965"></a>
 <a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.choosing_the_right_parameters">Choosing
 the Right Parameters</a>
 </h5>
@@ -535,7 +535,7 @@
 is exact, and so isn't used for the gamma function.
 
<a name="math_toolkit.backgrounders.lanczos.references"></a><h5>
-<a name="id1278738"></a>
+<a name="id1384504"></a>
 <a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.references">References</a>
 </h5>
<a name="godfrey"></a><a name="pugh"></a><div class="orderedlist"><ol type="1">

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,10 +24,10 @@
</div>
<div class="section" lang="en">
<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>
+<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="id1279972"></a>
+<a name="id1385428"></a>
 <a class="link" href="refs.html#math_toolkit.backgrounders.refs.general_references">General
 references</a>
 </h5>
@@ -85,7 +85,7 @@
 Library (version 2), Walter E. Brown</a>
 
<a name="math_toolkit.backgrounders.refs.calculators"></a><h5>
-<a name="id1280059"></a>
+<a name="id1385516"></a>
 <a class="link" href="refs.html#math_toolkit.backgrounders.refs.calculators">Calculators</a>
 </h5>

@@ -107,7 +107,7 @@
 Binomial Probability Distribution Calculator.
 
<a name="math_toolkit.backgrounders.refs.other_libraries"></a><h5>
-<a name="id1280105"></a>
+<a name="id1385561"></a>
 <a class="link" href="refs.html#math_toolkit.backgrounders.refs.other_libraries">Other Libraries</a>
 </h5>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h3 class="title">
-<a name="math_toolkit.backgrounders.relative_error"></a><a class="link" href="relative_error.html" title="Relative Error">Relative Error</a>
+<a name="math_toolkit.backgrounders.relative_error"></a><a class="link" href="relative_error.html" title="Relative Error"> Relative
+ Error</a>
</h3></div></div></div>

 Given an actual value a and a found value v
@@ -77,8 +78,10 @@
 errors differ by a factor of 2, can actually be accurate to the same number
 of binary digits. You have been warned!
 
-<a name="zero_error"></a><a name="math_toolkit.backgrounders.relative_error.the_impossibility_of_zero_error"></a><h5>
-<a name="id1277549"></a>
+<a name="zero_error"></a>
+ 
+<a name="math_toolkit.backgrounders.relative_error.the_impossibility_of_zero_error"></a><h5>
+<a name="id1382032"></a>
 <a class="link" href="relative_error.html#math_toolkit.backgrounders.relative_error.the_impossibility_of_zero_error">The
 Impossibility of Zero Error</a>
 </h5>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h3 class="title">
-<a name="math_toolkit.backgrounders.remez"></a><a class="link" href="remez.html" title="The Remez Method">The Remez Method</a>
+<a name="math_toolkit.backgrounders.remez"></a><a class="link" href="remez.html" title="The Remez Method"> The Remez Method</a>
</h3></div></div></div>

 The Remez algorithm
@@ -94,7 +94,7 @@
 are located!
 
<a name="math_toolkit.backgrounders.remez.the_remez_method"></a><h5>
-<a name="id1278923"></a>
+<a name="id1384689"></a>
 <a class="link" href="remez.html#math_toolkit.backgrounders.remez.the_remez_method">The Remez
 Method</a>
 </h5>
@@ -174,7 +174,7 @@
</td></tr>
</table></div>
<a name="math_toolkit.backgrounders.remez.remez_step_1"></a><h5>
-<a name="id1279074"></a>
+<a name="id1384840"></a>
 <a class="link" href="remez.html#math_toolkit.backgrounders.remez.remez_step_1">Remez Step
 1</a>
 </h5>
@@ -205,7 +205,7 @@
 to 5.6x10-4.
 
<a name="math_toolkit.backgrounders.remez.remez_step_2"></a><h5>
-<a name="id1279148"></a>
+<a name="id1384914"></a>
 <a class="link" href="remez.html#math_toolkit.backgrounders.remez.remez_step_2">Remez Step
 2</a>
 </h5>
@@ -234,7 +234,7 @@
 In our example we perform multi-point exchange.
 
<a name="math_toolkit.backgrounders.remez.iteration"></a><h5>
-<a name="id1279181"></a>
+<a name="id1384947"></a>
 <a class="link" href="remez.html#math_toolkit.backgrounders.remez.iteration">Iteration</a>
 </h5>

@@ -250,7 +250,7 @@
 <img src="../../../graphs/remez-4.png" alt="remez-4">
 
<a name="math_toolkit.backgrounders.remez.rational_approximations"></a><h5>
-<a name="id1279225"></a>
+<a name="id1384991"></a>
 <a class="link" href="remez.html#math_toolkit.backgrounders.remez.rational_approximations">Rational
 Approximations</a>
 </h5>
@@ -299,7 +299,7 @@
 number of terms overall.
 
<a name="math_toolkit.backgrounders.remez.practical_considerations"></a><h5>
-<a name="id1279304"></a>
+<a name="id1385070"></a>
 <a class="link" href="remez.html#math_toolkit.backgrounders.remez.practical_considerations">Practical
 Considerations</a>
 </h5>
@@ -407,7 +407,7 @@
 desired minimax solution (5x10-4).
 
<a name="math_toolkit.backgrounders.remez.remez_method_checklist"></a><h5>
-<a name="id1279770"></a>
+<a name="id1385226"></a>
 <a class="link" href="remez.html#math_toolkit.backgrounders.remez.remez_method_checklist">Remez
 Method Checklist</a>
 </h5>
@@ -461,7 +461,7 @@
 </li>
</ul></div>
<a name="math_toolkit.backgrounders.remez.references"></a><h5>
-<a name="id1279852"></a>
+<a name="id1385308"></a>
 <a class="link" href="remez.html#math_toolkit.backgrounders.remez.references">References</a>
 </h5>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,183 +24,186 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
-<a name="math_toolkit.dist"></a><a class="link" href="dist.html" title="Statistical Distributions and Functions">Statistical Distributions and Functions</a>
+<a name="math_toolkit.dist"></a><a class="link" href="dist.html" title="Statistical Distributions and Functions"> Statistical Distributions and Functions</a>
</h2></div></div></div>
<div class="toc"><dl>
-<dt><a href="dist/stat_tut.html">Statistical Distributions
+<dt><a href="dist/stat_tut.html"> Statistical Distributions
 Tutorial</a></dt>
<dd><dl>
-<dt>Overview of Distributions</dt>
+<dt> Overview of Distributions</dt>
<dd><dl>
-<dt><a href="dist/stat_tut/overview/headers.html">Headers
+<dt><a href="dist/stat_tut/overview/headers.html"> Headers
 and Namespaces</a></dt>
-<dt><a href="dist/stat_tut/overview/objects.html">Distributions
+<dt><a href="dist/stat_tut/overview/objects.html"> Distributions
 are Objects</a></dt>
-<dt><a href="dist/stat_tut/overview/generic.html">Generic
+<dt><a href="dist/stat_tut/overview/generic.html"> Generic
 operations common to all distributions are non-member functions</a></dt>
-<dt><a href="dist/stat_tut/overview/complements.html">Complements
- are supported too - and when to use them</a></dt>
-<dt><a href="dist/stat_tut/overview/parameters.html">Parameters
- can be calculated</a></dt>
-<dt>Summary</dt>
-</dl></dd>
-<dt>Worked Examples</dt>
-<dd><dl>
-<dt><a href="dist/stat_tut/weg/dist_construct_eg.html">Distribution
- Construction Example</a></dt>
-<dt><a href="dist/stat_tut/weg/st_eg.html">Student's t
- Distribution Examples</a></dt>
-<dd><dl>
-<dt><a href="dist/stat_tut/weg/st_eg/tut_mean_intervals.html">Calculating
- confidence intervals on the mean with the Students-t distribution</a></dt>
-<dt><a href="dist/stat_tut/weg/st_eg/tut_mean_test.html">Testing
- a sample mean for difference from a "true" mean</a></dt>
-<dt><a href="dist/stat_tut/weg/st_eg/tut_mean_size.html">Estimating
- how large a sample size would have to become in order to give a significant
- Students-t test result with a single sample test</a></dt>
-<dt><a href="dist/stat_tut/weg/st_eg/two_sample_students_t.html">Comparing
- the means of two samples with the Students-t test</a></dt>
-<dt><a href="dist/stat_tut/weg/st_eg/paired_st.html">Comparing
- two paired samples with the Student's t distribution</a></dt>
+<dt><a href="dist/stat_tut/overview/complements.html">
+ Complements are supported too - and when to use them</a></dt>
+<dt><a href="dist/stat_tut/overview/parameters.html">
+ Parameters can be calculated</a></dt>
+<dt> Summary</dt>
+</dl></dd>
+<dt> Worked Examples</dt>
+<dd><dl>
+<dt><a href="dist/stat_tut/weg/dist_construct_eg.html">
+ Distribution Construction Example</a></dt>
+<dt><a href="dist/stat_tut/weg/st_eg.html"> Student's
+ t Distribution Examples</a></dt>
+<dd><dl>
+<dt><a href="dist/stat_tut/weg/st_eg/tut_mean_intervals.html">
+ Calculating confidence intervals on the mean with the Students-t distribution</a></dt>
+<dt><a href="dist/stat_tut/weg/st_eg/tut_mean_test.html">
+ Testing a sample mean for difference from a "true" mean</a></dt>
+<dt><a href="dist/stat_tut/weg/st_eg/tut_mean_size.html">
+ Estimating how large a sample size would have to become in order to give
+ a significant Students-t test result with a single sample test</a></dt>
+<dt><a href="dist/stat_tut/weg/st_eg/two_sample_students_t.html">
+ Comparing the means of two samples with the Students-t test</a></dt>
+<dt><a href="dist/stat_tut/weg/st_eg/paired_st.html">
+ Comparing two paired samples with the Student's t distribution</a></dt>
</dl></dd>
-<dt><a href="dist/stat_tut/weg/cs_eg.html">Chi Squared
+<dt><a href="dist/stat_tut/weg/cs_eg.html"> Chi Squared
 Distribution Examples</a></dt>
<dd><dl>
-<dt><a href="dist/stat_tut/weg/cs_eg/chi_sq_intervals.html">Confidence
- Intervals on the Standard Deviation</a></dt>
-<dt><a href="dist/stat_tut/weg/cs_eg/chi_sq_test.html">Chi-Square
- Test for the Standard Deviation</a></dt>
-<dt><a href="dist/stat_tut/weg/cs_eg/chi_sq_size.html">Estimating
- the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</a></dt>
+<dt><a href="dist/stat_tut/weg/cs_eg/chi_sq_intervals.html">
+ Confidence Intervals on the Standard Deviation</a></dt>
+<dt><a href="dist/stat_tut/weg/cs_eg/chi_sq_test.html">
+ Chi-Square Test for the Standard Deviation</a></dt>
+<dt><a href="dist/stat_tut/weg/cs_eg/chi_sq_size.html">
+ Estimating the Required Sample Sizes for a Chi-Square Test for the Standard
+ Deviation</a></dt>
</dl></dd>
-<dt><a href="dist/stat_tut/weg/f_eg.html">F Distribution
+<dt><a href="dist/stat_tut/weg/f_eg.html"> F Distribution
 Examples</a></dt>
-<dt><a href="dist/stat_tut/weg/binom_eg.html">Binomial
+<dt><a href="dist/stat_tut/weg/binom_eg.html"> Binomial
 Distribution Examples</a></dt>
<dd><dl>
-<dt><a href="dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html">Binomial
- Coin-Flipping Example</a></dt>
-<dt><a href="dist/stat_tut/weg/binom_eg/binomial_quiz_example.html">Binomial
- Quiz Example</a></dt>
-<dt><a href="dist/stat_tut/weg/binom_eg/binom_conf.html">Calculating
- Confidence Limits on the Frequency of Occurrence for a Binomial Distribution</a></dt>
-<dt><a href="dist/stat_tut/weg/binom_eg/binom_size_eg.html">Estimating
- Sample Sizes for a Binomial Distribution.</a></dt>
+<dt><a href="dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html">
+ Binomial Coin-Flipping Example</a></dt>
+<dt><a href="dist/stat_tut/weg/binom_eg/binomial_quiz_example.html">
+ Binomial Quiz Example</a></dt>
+<dt><a href="dist/stat_tut/weg/binom_eg/binom_conf.html">
+ Calculating Confidence Limits on the Frequency of Occurrence for a Binomial
+ Distribution</a></dt>
+<dt><a href="dist/stat_tut/weg/binom_eg/binom_size_eg.html">
+ Estimating Sample Sizes for a Binomial Distribution.</a></dt>
</dl></dd>
-<dt><a href="dist/stat_tut/weg/geometric_eg.html">Geometric
+<dt><a href="dist/stat_tut/weg/geometric_eg.html"> Geometric
 Distribution Examples</a></dt>
-<dt><a href="dist/stat_tut/weg/neg_binom_eg.html">Negative
+<dt><a href="dist/stat_tut/weg/neg_binom_eg.html"> Negative
 Binomial Distribution Examples</a></dt>
<dd><dl>
-<dt><a href="dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html">Calculating
- Confidence Limits on the Frequency of Occurrence for the Negative Binomial
- Distribution</a></dt>
-<dt><a href="dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html">Estimating
- Sample Sizes for the Negative Binomial.</a></dt>
-<dt><a href="dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html">Negative
- Binomial Sales Quota Example.</a></dt>
-<dt><a href="dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html">Negative
- Binomial Table Printing Example.</a></dt>
+<dt><a href="dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html">
+ Calculating Confidence Limits on the Frequency of Occurrence for the
+ Negative Binomial Distribution</a></dt>
+<dt><a href="dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html">
+ Estimating Sample Sizes for the Negative Binomial.</a></dt>
+<dt><a href="dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html">
+ Negative Binomial Sales Quota Example.</a></dt>
+<dt><a href="dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html">
+ Negative Binomial Table Printing Example.</a></dt>
</dl></dd>
-<dt><a href="dist/stat_tut/weg/normal_example.html">Normal
+<dt><a href="dist/stat_tut/weg/normal_example.html"> Normal
 Distribution Examples</a></dt>
-<dd><dl><dt><a href="dist/stat_tut/weg/normal_example/normal_misc.html">Some
- Miscellaneous Examples of the Normal (Gaussian) Distribution</a></dt></dl></dd>
-<dt><a href="dist/stat_tut/weg/nccs_eg.html">Non Central
+<dd><dl><dt><a href="dist/stat_tut/weg/normal_example/normal_misc.html">
+ Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></dt></dl></dd>
+<dt><a href="dist/stat_tut/weg/nccs_eg.html"> Non Central
 Chi Squared Example</a></dt>
-<dd><dl><dt><a href="dist/stat_tut/weg/nccs_eg/nccs_power_eg.html">Tables
- of the power function of the χ2 test.</a></dt></dl></dd>
-<dt><a href="dist/stat_tut/weg/error_eg.html">Error Handling
+<dd><dl><dt><a href="dist/stat_tut/weg/nccs_eg/nccs_power_eg.html">
+ Tables of the power function of the χ2 test.</a></dt></dl></dd>
+<dt><a href="dist/stat_tut/weg/error_eg.html"> Error Handling
 Example</a></dt>
-<dt><a href="dist/stat_tut/weg/find_eg.html">Find Location
+<dt><a href="dist/stat_tut/weg/find_eg.html"> Find Location
 and Scale Examples</a></dt>
<dd><dl>
-<dt><a href="dist/stat_tut/weg/find_eg/find_location_eg.html">Find
- Location (Mean) Example</a></dt>
-<dt><a href="dist/stat_tut/weg/find_eg/find_scale_eg.html">Find
- Scale (Standard Deviation) Example</a></dt>
-<dt><a href="dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html">Find
- mean and standard deviation example</a></dt>
+<dt><a href="dist/stat_tut/weg/find_eg/find_location_eg.html">
+ Find Location (Mean) Example</a></dt>
+<dt><a href="dist/stat_tut/weg/find_eg/find_scale_eg.html">
+ Find Scale (Standard Deviation) Example</a></dt>
+<dt><a href="dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html">
+ Find mean and standard deviation example</a></dt>
</dl></dd>
-<dt><a href="dist/stat_tut/weg/nag_library.html">Comparison
+<dt><a href="dist/stat_tut/weg/nag_library.html"> Comparison
 with C, R, FORTRAN-style Free Functions</a></dt>
-<dt><a href="dist/stat_tut/weg/c_sharp.html">Using the
+<dt><a href="dist/stat_tut/weg/c_sharp.html"> Using the
 Distributions from Within C#</a></dt>
</dl></dd>
-<dt><a href="dist/stat_tut/variates.html">Random Variates
+<dt><a href="dist/stat_tut/variates.html"> Random Variates
 and Distribution Parameters</a></dt>
-<dt><a href="dist/stat_tut/dist_params.html">Discrete Probability
+<dt><a href="dist/stat_tut/dist_params.html"> Discrete Probability
 Distributions</a></dt>
</dl></dd>
-<dt><a href="dist/dist_ref.html">Statistical Distributions
+<dt><a href="dist/dist_ref.html"> Statistical Distributions
 Reference</a></dt>
<dd><dl>
-<dt>Non-Member Properties</dt>
-<dt>Distributions</dt>
+<dt> Non-Member Properties</dt>
+<dt> Distributions</dt>
<dd><dl>
-<dt><a href="dist/dist_ref/dists/bernoulli_dist.html">Bernoulli
- Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/beta_dist.html">Beta
- Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/binomial_dist.html">Binomial
+<dt><a href="dist/dist_ref/dists/bernoulli_dist.html">
+ Bernoulli Distribution</a></dt>
+<dt><a href="dist/dist_ref/dists/beta_dist.html"> Beta
 Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/cauchy_dist.html">Cauchy-Lorentz
+<dt><a href="dist/dist_ref/dists/binomial_dist.html">
+ Binomial Distribution</a></dt>
+<dt><a href="dist/dist_ref/dists/cauchy_dist.html"> Cauchy-Lorentz
 Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/chi_squared_dist.html">Chi
- Squared Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/exp_dist.html">Exponential
+<dt><a href="dist/dist_ref/dists/chi_squared_dist.html">
+ Chi Squared Distribution</a></dt>
+<dt><a href="dist/dist_ref/dists/exp_dist.html"> Exponential
 Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/extreme_dist.html">Extreme
+<dt><a href="dist/dist_ref/dists/extreme_dist.html"> Extreme
 Value Distribution</a></dt>
-<dt>F Distribution</dt>
-<dt><a href="dist/dist_ref/dists/gamma_dist.html">Gamma
+<dt> F Distribution</dt>
+<dt><a href="dist/dist_ref/dists/gamma_dist.html"> Gamma
 (and Erlang) Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/geometric_dist.html">Geometric
- Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/hypergeometric_dist.html">Hypergeometric
- Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/inverse_chi_squared_dist.html">Inverse
- Chi Squared Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/inverse_gamma_dist.html">Inverse
- Gamma Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/inverse_gaussian_dist.html">Inverse
- Gaussian (or Inverse Normal) Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/laplace_dist.html">Laplace
- Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/logistic_dist.html">Logistic
- Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/lognormal_dist.html">Log
- Normal Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/negative_binomial_dist.html">Negative
- Binomial Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/nc_beta_dist.html">Noncentral
+<dt><a href="dist/dist_ref/dists/geometric_dist.html">
+ Geometric Distribution</a></dt>
+<dt><a href="dist/dist_ref/dists/hypergeometric_dist.html">
+ Hypergeometric Distribution</a></dt>
+<dt><a href="dist/dist_ref/dists/inverse_chi_squared_dist.html">
+ Inverse Chi Squared Distribution</a></dt>
+<dt><a href="dist/dist_ref/dists/inverse_gamma_dist.html">
+ Inverse Gamma Distribution</a></dt>
+<dt><a href="dist/dist_ref/dists/inverse_gaussian_dist.html">
+ Inverse Gaussian (or Inverse Normal) Distribution</a></dt>
+<dt><a href="dist/dist_ref/dists/laplace_dist.html"> Laplace
+ Distribution</a></dt>
+<dt><a href="dist/dist_ref/dists/logistic_dist.html">
+ Logistic Distribution</a></dt>
+<dt><a href="dist/dist_ref/dists/lognormal_dist.html">
+ Log Normal Distribution</a></dt>
+<dt><a href="dist/dist_ref/dists/negative_binomial_dist.html">
+ Negative Binomial Distribution</a></dt>
+<dt><a href="dist/dist_ref/dists/nc_beta_dist.html"> Noncentral
 Beta Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/nc_chi_squared_dist.html">Noncentral
- Chi-Squared Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/nc_f_dist.html">Noncentral
+<dt><a href="dist/dist_ref/dists/nc_chi_squared_dist.html">
+ Noncentral Chi-Squared Distribution</a></dt>
+<dt><a href="dist/dist_ref/dists/nc_f_dist.html"> Noncentral
 F Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/nc_t_dist.html">Noncentral
+<dt><a href="dist/dist_ref/dists/nc_t_dist.html"> Noncentral
 T Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/normal_dist.html">Normal
+<dt><a href="dist/dist_ref/dists/normal_dist.html"> Normal
 (Gaussian) Distribution</a></dt>
-<dt>Pareto Distribution</dt>
-<dt><a href="dist/dist_ref/dists/poisson_dist.html">Poisson
+<dt><a href="dist/dist_ref/dists/pareto.html"> Pareto
 Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/rayleigh.html">Rayleigh
+<dt><a href="dist/dist_ref/dists/poisson_dist.html"> Poisson
 Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/students_t_dist.html">Students
- t Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/triangular_dist.html">Triangular
+<dt><a href="dist/dist_ref/dists/rayleigh.html"> Rayleigh
 Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/uniform_dist.html">Uniform
+<dt><a href="dist/dist_ref/dists/students_t_dist.html">
+ Students t Distribution</a></dt>
+<dt><a href="dist/dist_ref/dists/triangular_dist.html">
+ Triangular Distribution</a></dt>
+<dt><a href="dist/dist_ref/dists/uniform_dist.html"> Uniform
 Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/weibull_dist.html">Weibull
+<dt><a href="dist/dist_ref/dists/weibull_dist.html"> Weibull
 Distribution</a></dt>
</dl></dd>
-<dt><a href="dist/dist_ref/dist_algorithms.html">Distribution
+<dt><a href="dist/dist_ref/dist_algorithms.html"> Distribution
 Algorithms</a></dt>
</dl></dd>
-<dt>Extras/Future Directions</dt>
+<dt> Extras/Future Directions</dt>
</dl></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,73 +24,74 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h3 class="title">
-<a name="math_toolkit.dist.dist_ref"></a><a class="link" href="dist_ref.html" title="Statistical Distributions Reference">Statistical Distributions
+<a name="math_toolkit.dist.dist_ref"></a><a class="link" href="dist_ref.html" title="Statistical Distributions Reference"> Statistical Distributions
 Reference</a>
</h3></div></div></div>
<div class="toc"><dl>
-<dt>Non-Member Properties</dt>
-<dt>Distributions</dt>
+<dt> Non-Member Properties</dt>
+<dt> Distributions</dt>
<dd><dl>
-<dt><a href="dist_ref/dists/bernoulli_dist.html">Bernoulli
+<dt><a href="dist_ref/dists/bernoulli_dist.html">
+ Bernoulli Distribution</a></dt>
+<dt><a href="dist_ref/dists/beta_dist.html"> Beta
 Distribution</a></dt>
-<dt><a href="dist_ref/dists/beta_dist.html">Beta
- Distribution</a></dt>
-<dt><a href="dist_ref/dists/binomial_dist.html">Binomial
- Distribution</a></dt>
-<dt><a href="dist_ref/dists/cauchy_dist.html">Cauchy-Lorentz
+<dt><a href="dist_ref/dists/binomial_dist.html">
+ Binomial Distribution</a></dt>
+<dt><a href="dist_ref/dists/cauchy_dist.html"> Cauchy-Lorentz
 Distribution</a></dt>
-<dt><a href="dist_ref/dists/chi_squared_dist.html">Chi
- Squared Distribution</a></dt>
-<dt><a href="dist_ref/dists/exp_dist.html">Exponential
+<dt><a href="dist_ref/dists/chi_squared_dist.html">
+ Chi Squared Distribution</a></dt>
+<dt><a href="dist_ref/dists/exp_dist.html"> Exponential
 Distribution</a></dt>
-<dt><a href="dist_ref/dists/extreme_dist.html">Extreme
+<dt><a href="dist_ref/dists/extreme_dist.html"> Extreme
 Value Distribution</a></dt>
-<dt>F Distribution</dt>
-<dt><a href="dist_ref/dists/gamma_dist.html">Gamma
+<dt> F Distribution</dt>
+<dt><a href="dist_ref/dists/gamma_dist.html"> Gamma
 (and Erlang) Distribution</a></dt>
-<dt><a href="dist_ref/dists/geometric_dist.html">Geometric
- Distribution</a></dt>
-<dt><a href="dist_ref/dists/hypergeometric_dist.html">Hypergeometric
- Distribution</a></dt>
-<dt><a href="dist_ref/dists/inverse_chi_squared_dist.html">Inverse
- Chi Squared Distribution</a></dt>
-<dt><a href="dist_ref/dists/inverse_gamma_dist.html">Inverse
- Gamma Distribution</a></dt>
-<dt><a href="dist_ref/dists/inverse_gaussian_dist.html">Inverse
- Gaussian (or Inverse Normal) Distribution</a></dt>
-<dt><a href="dist_ref/dists/laplace_dist.html">Laplace
- Distribution</a></dt>
-<dt><a href="dist_ref/dists/logistic_dist.html">Logistic
- Distribution</a></dt>
-<dt><a href="dist_ref/dists/lognormal_dist.html">Log
- Normal Distribution</a></dt>
-<dt><a href="dist_ref/dists/negative_binomial_dist.html">Negative
- Binomial Distribution</a></dt>
-<dt><a href="dist_ref/dists/nc_beta_dist.html">Noncentral
+<dt><a href="dist_ref/dists/geometric_dist.html">
+ Geometric Distribution</a></dt>
+<dt><a href="dist_ref/dists/hypergeometric_dist.html">
+ Hypergeometric Distribution</a></dt>
+<dt><a href="dist_ref/dists/inverse_chi_squared_dist.html">
+ Inverse Chi Squared Distribution</a></dt>
+<dt><a href="dist_ref/dists/inverse_gamma_dist.html">
+ Inverse Gamma Distribution</a></dt>
+<dt><a href="dist_ref/dists/inverse_gaussian_dist.html">
+ Inverse Gaussian (or Inverse Normal) Distribution</a></dt>
+<dt><a href="dist_ref/dists/laplace_dist.html"> Laplace
+ Distribution</a></dt>
+<dt><a href="dist_ref/dists/logistic_dist.html">
+ Logistic Distribution</a></dt>
+<dt><a href="dist_ref/dists/lognormal_dist.html">
+ Log Normal Distribution</a></dt>
+<dt><a href="dist_ref/dists/negative_binomial_dist.html">
+ Negative Binomial Distribution</a></dt>
+<dt><a href="dist_ref/dists/nc_beta_dist.html"> Noncentral
 Beta Distribution</a></dt>
-<dt><a href="dist_ref/dists/nc_chi_squared_dist.html">Noncentral
- Chi-Squared Distribution</a></dt>
-<dt><a href="dist_ref/dists/nc_f_dist.html">Noncentral
+<dt><a href="dist_ref/dists/nc_chi_squared_dist.html">
+ Noncentral Chi-Squared Distribution</a></dt>
+<dt><a href="dist_ref/dists/nc_f_dist.html"> Noncentral
 F Distribution</a></dt>
-<dt><a href="dist_ref/dists/nc_t_dist.html">Noncentral
+<dt><a href="dist_ref/dists/nc_t_dist.html"> Noncentral
 T Distribution</a></dt>
-<dt><a href="dist_ref/dists/normal_dist.html">Normal
+<dt><a href="dist_ref/dists/normal_dist.html"> Normal
 (Gaussian) Distribution</a></dt>
-<dt>Pareto Distribution</dt>
-<dt><a href="dist_ref/dists/poisson_dist.html">Poisson
+<dt><a href="dist_ref/dists/pareto.html"> Pareto
 Distribution</a></dt>
-<dt><a href="dist_ref/dists/rayleigh.html">Rayleigh
+<dt><a href="dist_ref/dists/poisson_dist.html"> Poisson
 Distribution</a></dt>
-<dt><a href="dist_ref/dists/students_t_dist.html">Students
- t Distribution</a></dt>
-<dt><a href="dist_ref/dists/triangular_dist.html">Triangular
+<dt><a href="dist_ref/dists/rayleigh.html"> Rayleigh
 Distribution</a></dt>
-<dt><a href="dist_ref/dists/uniform_dist.html">Uniform
+<dt><a href="dist_ref/dists/students_t_dist.html">
+ Students t Distribution</a></dt>
+<dt><a href="dist_ref/dists/triangular_dist.html">
+ Triangular Distribution</a></dt>
+<dt><a href="dist_ref/dists/uniform_dist.html"> Uniform
 Distribution</a></dt>
-<dt><a href="dist_ref/dists/weibull_dist.html">Weibull
+<dt><a href="dist_ref/dists/weibull_dist.html"> Weibull
 Distribution</a></dt>
</dl></dd>
-<dt><a href="dist_ref/dist_algorithms.html">Distribution
+<dt><a href="dist_ref/dist_algorithms.html"> Distribution
 Algorithms</a></dt>
</dl></div>
</div>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,11 +24,11 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h4 class="title">
-<a name="math_toolkit.dist.dist_ref.dist_algorithms"></a><a class="link" href="dist_algorithms.html" title="Distribution Algorithms">Distribution
+<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="id1048899"></a>
+<a name="id1156159"></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
 the Location and Scale for Normal and similar distributions</a>
 </h5>
@@ -50,7 +50,7 @@
using boost::math::complement; // Will be needed by users who want to use complements.
</pre>
<a name="math_toolkit.dist.dist_ref.dist_algorithms.find_location_function"></a><h5>
-<a name="id1049027"></a>
+<a name="id1156258"></a>
 <a class="link" href="dist_algorithms.html#math_toolkit.dist.dist_ref.dist_algorithms.find_location_function">find_location
 function</a>
 </h5>
@@ -80,7 +80,7 @@
 }} // namespaces
</pre>
<a name="math_toolkit.dist.dist_ref.dist_algorithms.find_scale_function"></a><h5>
-<a name="id1049472"></a>
+<a name="id1156703"></a>
 <a class="link" href="dist_algorithms.html#math_toolkit.dist.dist_ref.dist_algorithms.find_scale_function">find_scale
 function</a>
 </h5>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,66 +24,67 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h4 class="title">
-<a name="math_toolkit.dist.dist_ref.dists"></a><a class="link" href="dists.html" title="Distributions">Distributions</a>
+<a name="math_toolkit.dist.dist_ref.dists"></a><a class="link" href="dists.html" title="Distributions"> Distributions</a>
</h4></div></div></div>
<div class="toc"><dl>
-<dt><a href="dists/bernoulli_dist.html">Bernoulli
+<dt><a href="dists/bernoulli_dist.html">
+ Bernoulli Distribution</a></dt>
+<dt><a href="dists/beta_dist.html"> Beta
 Distribution</a></dt>
-<dt><a href="dists/beta_dist.html">Beta
- Distribution</a></dt>
-<dt><a href="dists/binomial_dist.html">Binomial
- Distribution</a></dt>
-<dt><a href="dists/cauchy_dist.html">Cauchy-Lorentz
+<dt><a href="dists/binomial_dist.html">
+ Binomial Distribution</a></dt>
+<dt><a href="dists/cauchy_dist.html"> Cauchy-Lorentz
 Distribution</a></dt>
-<dt><a href="dists/chi_squared_dist.html">Chi
- Squared Distribution</a></dt>
-<dt><a href="dists/exp_dist.html">Exponential
+<dt><a href="dists/chi_squared_dist.html">
+ Chi Squared Distribution</a></dt>
+<dt><a href="dists/exp_dist.html"> Exponential
 Distribution</a></dt>
-<dt><a href="dists/extreme_dist.html">Extreme
+<dt><a href="dists/extreme_dist.html"> Extreme
 Value Distribution</a></dt>
-<dt>F Distribution</dt>
-<dt><a href="dists/gamma_dist.html">Gamma
+<dt> F Distribution</dt>
+<dt><a href="dists/gamma_dist.html"> Gamma
 (and Erlang) Distribution</a></dt>
-<dt><a href="dists/geometric_dist.html">Geometric
- Distribution</a></dt>
-<dt><a href="dists/hypergeometric_dist.html">Hypergeometric
- Distribution</a></dt>
-<dt><a href="dists/inverse_chi_squared_dist.html">Inverse
- Chi Squared Distribution</a></dt>
-<dt><a href="dists/inverse_gamma_dist.html">Inverse
- Gamma Distribution</a></dt>
-<dt><a href="dists/inverse_gaussian_dist.html">Inverse
- Gaussian (or Inverse Normal) Distribution</a></dt>
-<dt><a href="dists/laplace_dist.html">Laplace
- Distribution</a></dt>
-<dt><a href="dists/logistic_dist.html">Logistic
- Distribution</a></dt>
-<dt><a href="dists/lognormal_dist.html">Log
- Normal Distribution</a></dt>
-<dt><a href="dists/negative_binomial_dist.html">Negative
- Binomial Distribution</a></dt>
-<dt><a href="dists/nc_beta_dist.html">Noncentral
+<dt><a href="dists/geometric_dist.html">
+ Geometric Distribution</a></dt>
+<dt><a href="dists/hypergeometric_dist.html">
+ Hypergeometric Distribution</a></dt>
+<dt><a href="dists/inverse_chi_squared_dist.html">
+ Inverse Chi Squared Distribution</a></dt>
+<dt><a href="dists/inverse_gamma_dist.html">
+ Inverse Gamma Distribution</a></dt>
+<dt><a href="dists/inverse_gaussian_dist.html">
+ Inverse Gaussian (or Inverse Normal) Distribution</a></dt>
+<dt><a href="dists/laplace_dist.html"> Laplace
+ Distribution</a></dt>
+<dt><a href="dists/logistic_dist.html">
+ Logistic Distribution</a></dt>
+<dt><a href="dists/lognormal_dist.html">
+ Log Normal Distribution</a></dt>
+<dt><a href="dists/negative_binomial_dist.html">
+ Negative Binomial Distribution</a></dt>
+<dt><a href="dists/nc_beta_dist.html"> Noncentral
 Beta Distribution</a></dt>
-<dt><a href="dists/nc_chi_squared_dist.html">Noncentral
- Chi-Squared Distribution</a></dt>
-<dt><a href="dists/nc_f_dist.html">Noncentral
+<dt><a href="dists/nc_chi_squared_dist.html">
+ Noncentral Chi-Squared Distribution</a></dt>
+<dt><a href="dists/nc_f_dist.html"> Noncentral
 F Distribution</a></dt>
-<dt><a href="dists/nc_t_dist.html">Noncentral
+<dt><a href="dists/nc_t_dist.html"> Noncentral
 T Distribution</a></dt>
-<dt><a href="dists/normal_dist.html">Normal
+<dt><a href="dists/normal_dist.html"> Normal
 (Gaussian) Distribution</a></dt>
-<dt>Pareto Distribution</dt>
-<dt><a href="dists/poisson_dist.html">Poisson
+<dt><a href="dists/pareto.html"> Pareto
 Distribution</a></dt>
-<dt><a href="dists/rayleigh.html">Rayleigh
+<dt><a href="dists/poisson_dist.html"> Poisson
 Distribution</a></dt>
-<dt><a href="dists/students_t_dist.html">Students
- t Distribution</a></dt>
-<dt><a href="dists/triangular_dist.html">Triangular
+<dt><a href="dists/rayleigh.html"> Rayleigh
 Distribution</a></dt>
-<dt><a href="dists/uniform_dist.html">Uniform
+<dt><a href="dists/students_t_dist.html">
+ Students t Distribution</a></dt>
+<dt><a href="dists/triangular_dist.html">
+ Triangular Distribution</a></dt>
+<dt><a href="dists/uniform_dist.html"> Uniform
 Distribution</a></dt>
-<dt><a href="dists/weibull_dist.html">Weibull
+<dt><a href="dists/weibull_dist.html"> Weibull
 Distribution</a></dt>
</dl></div>
</div>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist"></a><a class="link" href="bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli
- Distribution</a>
+<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist"></a><a class="link" href="bernoulli_dist.html" title="Bernoulli Distribution">
+ Bernoulli Distribution</a>
</h5></div></div></div>


@@ -87,7 +87,7 @@
 <img src="../../../../../graphs/bernoulli_cdf.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.member_functions"></a><h5>
-<a name="id984516"></a>
+<a name="id1095040"></a>
 <a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -103,7 +103,7 @@
 Returns the success_fraction parameter of this distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.non_member_accessors"></a><h5>
-<a name="id984594"></a>
+<a name="id1095118"></a>
 <a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -128,7 +128,7 @@
 exception and make an error message available.
 
<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.accuracy"></a><h5>
-<a name="id984698"></a>
+<a name="id1095222"></a>
 <a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.accuracy">Accuracy</a>
 </h5>

@@ -136,7 +136,7 @@
 and so should have errors within an epsilon or two.
 
<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.implementation"></a><h5>
-<a name="id984719"></a>
+<a name="id1095243"></a>
 <a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.implementation">Implementation</a>
 </h5>

@@ -327,7 +327,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.references"></a><h5>
-<a name="id985048"></a>
+<a name="id1095572"></a>
 <a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.references">References</a>
 </h5>
<div class="itemizedlist"><ul type="disc">

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.beta_dist"></a><a class="link" href="beta_dist.html" title="Beta Distribution">Beta
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist"></a><a class="link" href="beta_dist.html" title="Beta Distribution"> Beta
 Distribution</a>
</h5></div></div></div>

@@ -132,12 +132,12 @@
 whose apex is away from the centre (where x = half).
 
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.member_functions"></a><h5>
-<a name="id985863"></a>
+<a name="id1096460"></a>
 <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="id985878"></a>
+<a name="id1096476"></a>
 <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.constructor">Constructor</a>
 </h6>
<pre class="programlisting">beta_distribution(RealType alpha, RealType beta);
@@ -164,7 +164,7 @@
 yellow in the graph above).
 
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.parameter_accessors"></a><h6>
-<a name="id985994"></a>
+<a name="id1096591"></a>
 <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.parameter_accessors">Parameter
 Accessors</a>
 </h6>
@@ -188,7 +188,7 @@
assert(mybeta.beta() == 5.); // mybeta.beta() returns 5
</pre>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.parameter_estimators"></a><h5>
-<a name="id986195"></a>
+<a name="id1096792"></a>
 <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.parameter_estimators">Parameter
 Estimators</a>
 </h5>
@@ -241,7 +241,7 @@
 Returns the value of β   that gives: <code class="computeroutput">cdf(beta_distribution<RealType>(alpha, beta), x) == probability</code>.
 
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.non_member_accessor_functions"></a><h5>
-<a name="id988421"></a>
+<a name="id1097242"></a>
 <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>
@@ -263,7 +263,7 @@
 Mathworld</a>.
 
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.applications"></a><h5>
-<a name="id988523"></a>
+<a name="id1097344"></a>
 <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.applications">Applications</a>
 </h5>

@@ -276,7 +276,7 @@
 statistical inference</a>.
 
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.related_distributions"></a><h5>
-<a name="id988548"></a>
+<a name="id1097370"></a>
 <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.related_distributions">Related
 distributions</a>
 </h5>
@@ -303,7 +303,7 @@
 Distribution</a> with its p parameter set to x.
 
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.accuracy"></a><h5>
-<a name="id988595"></a>
+<a name="id1097416"></a>
 <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.accuracy">Accuracy</a>
 </h5>

@@ -315,7 +315,7 @@
 please refer to these functions for information on accuracy.
 
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.implementation"></a><h5>
-<a name="id988639"></a>
+<a name="id1097461"></a>
 <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.implementation">Implementation</a>
 </h5>

@@ -500,6 +500,8 @@
 
 </td>
<td>
+ 
+ 
 </td>
</tr>
<tr>
@@ -594,7 +596,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.references"></a><h5>
-<a name="id989663"></a>
+<a name="id1098743"></a>
 <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.references">References</a>
 </h5>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.binomial_dist"></a><a class="link" href="binomial_dist.html" title="Binomial Distribution">Binomial
- Distribution</a>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist"></a><a class="link" href="binomial_dist.html" title="Binomial Distribution">
+ Binomial Distribution</a>
</h5></div></div></div>


@@ -127,6 +127,8 @@

 <img src="../../../../../graphs/binomial_pdf_2.png" align="middle">
 
+
+ 
<div class="caution"><table border="0" summary="Caution">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../../../doc/src/images/caution.png"></td>
@@ -134,39 +136,43 @@
</tr>
<tr><td align="left" valign="top">

- The Binomial distribution is a discrete distribution: internally, functions
- like the <code class="computeroutput">cdf</code> and <code class="computeroutput">pdf</code> are treated "as if"
- they are continuous functions, but in reality the results returned
- from these functions only have meaning if an integer value is provided
- for the random variate argument.
- 
-
- The quantile function will by default return an integer result that
- has been rounded outwards. That is to say lower
- quantiles (where the probability is less than 0.5) are rounded downward,
- and upper quantiles (where the probability is greater than 0.5) are
- rounded upwards. This behaviour ensures that if an X% quantile is requested,
- then at least the requested coverage will be present
- in the central region, and no more than the requested
- coverage will be present in the tails.
- 
-
- This behaviour can be changed so that the quantile functions are rounded
- differently, or even return a real-valued result using <a class="link" href="../../../policy/pol_overview.html" title="Policy Overview">Policies</a>.
- It is strongly recommended that you read the tutorial <a class="link" href="../../../policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
- Quantiles of Discrete Distributions</a> before using the quantile
- function on the Binomial distribution. The <a class="link" href="../../../policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">reference
- docs</a> describe how to change the rounding policy for these distributions.
- 
+ The Binomial distribution is a discrete distribution: internally,
+ functions like the <code class="computeroutput">cdf</code>
+ and <code class="computeroutput">pdf</code> are treated
+ "as if" they are continuous functions, but in reality the
+ results returned from these functions only have meaning if an integer
+ value is provided for the random variate argument.
+ 
+
+ The quantile function will by default return an integer result that
+ has been rounded outwards. That is to say lower
+ quantiles (where the probability is less than 0.5) are rounded downward,
+ and upper quantiles (where the probability is greater than 0.5) are
+ rounded upwards. This behaviour ensures that if an X% quantile is
+ requested, then at least the requested coverage
+ will be present in the central region, and no more than
+ the requested coverage will be present in the tails.
+ 
+
+ This behaviour can be changed so that the quantile functions are
+ rounded differently, or even return a real-valued result using <a class="link" href="../../../policy/pol_overview.html" title="Policy Overview">Policies</a>. It is
+ strongly recommended that you read the tutorial <a class="link" href="../../../policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
+ Quantiles of Discrete Distributions</a> before using the quantile
+ function on the Binomial distribution. The <a class="link" href="../../../policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">reference
+ docs</a> describe how to change the rounding policy for these
+ distributions.
+ 
</td></tr>
</table></div>
+
+ 
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.member_functions"></a><h5>
-<a name="id991920"></a>
+<a name="id1099693"></a>
 <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="id991938"></a>
+<a name="id1099711"></a>
 <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.construct">Construct</a>
 </h6>
<pre class="programlisting">binomial_distribution(RealType n, RealType p);
@@ -183,7 +189,7 @@
 otherwise calls <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
 
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.accessors"></a><h6>
-<a name="id992055"></a>
+<a name="id1099829"></a>
 <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.accessors">Accessors</a>
 </h6>
<pre class="programlisting">RealType success_fraction() const;
@@ -199,7 +205,7 @@
 was constructed.
 
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.lower_bound_on_the_success_fraction"></a><h6>
-<a name="id992136"></a>
+<a name="id1099909"></a>
 <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>
@@ -305,7 +311,7 @@
 limits illustrated in the case of the binomial. Biometrika 26 404-413.
 
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.upper_bound_on_the_success_fraction"></a><h6>
-<a name="id992589"></a>
+<a name="id1100363"></a>
 <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>
@@ -383,7 +389,7 @@
</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="id992905"></a>
+<a name="id1101856"></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
 the Number of Trials Required for a Certain Number of Successes</a>
 </h6>
@@ -425,7 +431,7 @@
 of seeing 10 events that occur with frequency one half.
 
<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="id993106"></a>
+<a name="id1102058"></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
 the Maximum Number of Trials to Ensure no more than a Certain Number
 of Successes</a>
@@ -473,7 +479,7 @@
 Worked Example.</a>
 
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.non_member_accessors"></a><h5>
-<a name="id993316"></a>
+<a name="id1102268"></a>
 <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -622,7 +628,7 @@
</table></div>
</div>
 <a name="math_toolkit.dist.dist_ref.dists.binomial_dist.examples"></a><h5>
-<a name="id994130"></a>
+<a name="id1102823"></a>
 <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.examples">Examples</a>
 </h5>

@@ -630,7 +636,7 @@
 examples</a> are available illustrating the use of the binomial distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.accuracy"></a><h5>
-<a name="id994152"></a>
+<a name="id1102845"></a>
 <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.accuracy">Accuracy</a>
 </h5>

@@ -640,7 +646,7 @@
 please refer to these functions for information on accuracy.
 
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.implementation"></a><h5>
-<a name="id994180"></a>
+<a name="id1102874"></a>
 <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.implementation">Implementation</a>
 </h5>

@@ -884,7 +890,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.references"></a><h5>
-<a name="id995230"></a>
+<a name="id1103943"></a>
 <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.references">References</a>
 </h5>
<div class="itemizedlist"><ul type="disc">

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist"></a><a class="link" href="cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz
+<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist"></a><a class="link" href="cauchy_dist.html" title="Cauchy-Lorentz Distribution"> Cauchy-Lorentz
 Distribution</a>
</h5></div></div></div>

@@ -88,7 +88,7 @@
 <img src="../../../../../graphs/cauchy_pdf2.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.member_functions"></a><h5>
-<a name="id995749"></a>
+<a name="id1104462"></a>
 <a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -114,7 +114,7 @@
 Returns the scale parameter of the distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.non_member_accessors"></a><h5>
-<a name="id995896"></a>
+<a name="id1104609"></a>
 <a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -148,7 +148,7 @@
 The domain of the random variable is [-[max_value], +[min_value]].
 
<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.accuracy"></a><h5>
-<a name="id996039"></a>
+<a name="id1104752"></a>
 <a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.accuracy">Accuracy</a>
 </h5>

@@ -157,7 +157,7 @@
 have very low error rates.
 
<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.implementation"></a><h5>
-<a name="id996073"></a>
+<a name="id1104786"></a>
 <a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.implementation">Implementation</a>
 </h5>

@@ -273,7 +273,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.references"></a><h5>
-<a name="id997539"></a>
+<a name="id1105012"></a>
 <a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.references">References</a>
 </h5>
<div class="itemizedlist"><ul type="disc">

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist"></a><a class="link" href="chi_squared_dist.html" title="Chi Squared Distribution">Chi
- Squared Distribution</a>
+<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist"></a><a class="link" href="chi_squared_dist.html" title="Chi Squared Distribution">
+ Chi Squared Distribution</a>
</h5></div></div></div>


@@ -87,7 +87,7 @@
 <img src="../../../../../graphs/chi_squared_pdf.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.member_functions"></a><h5>
-<a name="id998104"></a>
+<a name="id1105578"></a>
 <a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -170,7 +170,7 @@
 NIST Engineering Statistics Handbook, Section 7.2.3.2</a>.
 
<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.non_member_accessors"></a><h5>
-<a name="id998436"></a>
+<a name="id1105909"></a>
 <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>
@@ -196,7 +196,7 @@
 The domain of the random variable is [0, +∞].
 
<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.examples"></a><h5>
-<a name="id998539"></a>
+<a name="id1106716"></a>
 <a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.examples">Examples</a>
 </h5>

@@ -204,7 +204,7 @@
 are available illustrating the use of the Chi Squared Distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.accuracy"></a><h5>
-<a name="id998565"></a>
+<a name="id1106742"></a>
 <a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.accuracy">Accuracy</a>
 </h5>

@@ -212,7 +212,7 @@
 gamma functions</a>: please refer to the accuracy data for those functions.
 
<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.implementation"></a><h5>
-<a name="id998589"></a>
+<a name="id1106766"></a>
 <a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.implementation">Implementation</a>
 </h5>

@@ -379,7 +379,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.references"></a><h5>
-<a name="id998886"></a>
+<a name="id1107063"></a>
 <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 type="disc">

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.exp_dist"></a><a class="link" href="exp_dist.html" title="Exponential Distribution">Exponential
+<a name="math_toolkit.dist.dist_ref.dists.exp_dist"></a><a class="link" href="exp_dist.html" title="Exponential Distribution"> Exponential
 Distribution</a>
</h5></div></div></div>

@@ -71,7 +71,7 @@
 <img src="../../../../../graphs/exponential_pdf.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.exp_dist.member_functions"></a><h5>
-<a name="id999320"></a>
+<a name="id1107497"></a>
 <a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -91,7 +91,7 @@
 Accessor function returns the lambda parameter of the distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.exp_dist.non_member_accessors"></a><h5>
-<a name="id999421"></a>
+<a name="id1107598"></a>
 <a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -111,7 +111,7 @@
 The domain of the random variable is [0, +∞].
 
<a name="math_toolkit.dist.dist_ref.dists.exp_dist.accuracy"></a><h5>
-<a name="id999520"></a>
+<a name="id1107697"></a>
 <a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.accuracy">Accuracy</a>
 </h5>

@@ -122,7 +122,7 @@
 should have very low error rates.
 
<a name="math_toolkit.dist.dist_ref.dists.exp_dist.implementation"></a><h5>
-<a name="id999568"></a>
+<a name="id1107745"></a>
 <a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.implementation">Implementation</a>
 </h5>

@@ -283,7 +283,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.exp_dist.references"></a><h5>
-<a name="id1000612"></a>
+<a name="id1108012"></a>
 <a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.references">references</a>
 </h5>
<div class="itemizedlist"><ul type="disc">

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.extreme_dist"></a><a class="link" href="extreme_dist.html" title="Extreme Value Distribution">Extreme
+<a name="math_toolkit.dist.dist_ref.dists.extreme_dist"></a><a class="link" href="extreme_dist.html" title="Extreme Value Distribution"> Extreme
 Value Distribution</a>
</h5></div></div></div>

@@ -100,7 +100,7 @@
 <img src="../../../../../graphs/extreme_value_pdf2.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.member_functions"></a><h5>
-<a name="id1001175"></a>
+<a name="id1108575"></a>
 <a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -125,7 +125,7 @@
 Returns the scale parameter of the distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.non_member_accessors"></a><h5>
-<a name="id1001331"></a>
+<a name="id1108731"></a>
 <a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -145,7 +145,7 @@
 The domain of the random parameter is [-∞, +∞].
 
<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.accuracy"></a><h5>
-<a name="id1001428"></a>
+<a name="id1108828"></a>
 <a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.accuracy">Accuracy</a>
 </h5>

@@ -154,7 +154,7 @@
 very low error rates.
 
<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.implementation"></a><h5>
-<a name="id1001461"></a>
+<a name="id1110260"></a>
 <a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.implementation">Implementation</a>
 </h5>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.f_dist"></a><a class="link" href="f_dist.html" title="F Distribution">F Distribution</a>
+<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>


@@ -80,7 +80,7 @@
 <img src="../../../../../graphs/fisher_f_pdf.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.f_dist.member_functions"></a><h5>
-<a name="id1002225"></a>
+<a name="id1111023"></a>
 <a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -106,7 +106,7 @@
 Returns the denominator degrees of freedom parameter of the distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.f_dist.non_member_accessors"></a><h5>
-<a name="id1002378"></a>
+<a name="id1111176"></a>
 <a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -126,7 +126,7 @@
 The domain of the random variable is [0, +∞].
 
<a name="math_toolkit.dist.dist_ref.dists.f_dist.examples"></a><h5>
-<a name="id1002478"></a>
+<a name="id1111276"></a>
 <a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.examples">Examples</a>
 </h5>

@@ -134,7 +134,7 @@
 are available illustrating the use of the F Distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.f_dist.accuracy"></a><h5>
-<a name="id1002499"></a>
+<a name="id1111298"></a>
 <a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.accuracy">Accuracy</a>
 </h5>

@@ -143,7 +143,7 @@
 refer to those functions for accuracy data.
 
<a name="math_toolkit.dist.dist_ref.dists.f_dist.implementation"></a><h5>
-<a name="id1002526"></a>
+<a name="id1111324"></a>
 <a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.implementation">Implementation</a>
 </h5>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.gamma_dist"></a><a class="link" href="gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma
+<a name="math_toolkit.dist.dist_ref.dists.gamma_dist"></a><a class="link" href="gamma_dist.html" title="Gamma (and Erlang) Distribution"> Gamma
 (and Erlang) Distribution</a>
</h5></div></div></div>

@@ -137,7 +137,7 @@
 than a dedicated Erlang Distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.member_functions"></a><h5>
-<a name="id1003747"></a>
+<a name="id1112403"></a>
 <a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -162,7 +162,7 @@
 Returns the scale parameter of this distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.non_member_accessors"></a><h5>
-<a name="id1003892"></a>
+<a name="id1113257"></a>
 <a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -182,7 +182,7 @@
 The domain of the random variable is [0,+∞].
 
<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.accuracy"></a><h5>
-<a name="id1003989"></a>
+<a name="id1113354"></a>
 <a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.accuracy">Accuracy</a>
 </h5>

@@ -194,7 +194,7 @@
 refer to the accuracy data for those functions for more information.
 
<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.implementation"></a><h5>
-<a name="id1004028"></a>
+<a name="id1113392"></a>
 <a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.implementation">Implementation</a>
 </h5>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.geometric_dist"></a><a class="link" href="geometric_dist.html" title="Geometric Distribution">Geometric
- Distribution</a>
+<a name="math_toolkit.dist.dist_ref.dists.geometric_dist"></a><a class="link" href="geometric_dist.html" title="Geometric Distribution">
+ Geometric Distribution</a>
</h5></div></div></div>


@@ -146,7 +146,7 @@
 <img src="../../../../../graphs/geometric_cdf_discrete.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.related_distributions"></a><h5>
-<a name="id1006335"></a>
+<a name="id1114576"></a>
 <a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.related_distributions">Related
 Distributions</a>
 </h5>
@@ -171,6 +171,8 @@
 take integer values (floor or ceil functions) from functions that return
 a number of successes.
 
+
+ 
<div class="caution"><table border="0" summary="Caution">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../../../doc/src/images/caution.png"></td>
@@ -178,40 +180,43 @@
</tr>
<tr><td align="left" valign="top">

- The geometric distribution is a discrete distribution: internally,
- functions like the <code class="computeroutput">cdf</code>
- and <code class="computeroutput">pdf</code> are treated
- "as if" they are continuous functions, but in reality the
- results returned from these functions only have meaning if an integer
- value is provided for the random variate argument.
- 
-
- The quantile function will by default return an integer result that
- has been rounded outwards. That is to say lower
- quantiles (where the probability is less than 0.5) are rounded downward,
- and upper quantiles (where the probability is greater than 0.5) are
- rounded upwards. This behaviour ensures that if an X% quantile is requested,
- then at least the requested coverage will be present
- in the central region, and no more than the requested
- coverage will be present in the tails.
- 
-
- This behaviour can be changed so that the quantile functions are rounded
- differently, or even return a real-valued result using <a class="link" href="../../../policy/pol_overview.html" title="Policy Overview">Policies</a>.
- It is strongly recommended that you read the tutorial <a class="link" href="../../../policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
- Quantiles of Discrete Distributions</a> before using the quantile
- function on the geometric distribution. The <a class="link" href="../../../policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">reference
- docs</a> describe how to change the rounding policy for these distributions.
- 
+ The geometric distribution is a discrete distribution: internally,
+ functions like the <code class="computeroutput">cdf</code>
+ and <code class="computeroutput">pdf</code> are treated
+ "as if" they are continuous functions, but in reality the
+ results returned from these functions only have meaning if an integer
+ value is provided for the random variate argument.
+ 
+
+ The quantile function will by default return an integer result that
+ has been rounded outwards. That is to say lower
+ quantiles (where the probability is less than 0.5) are rounded downward,
+ and upper quantiles (where the probability is greater than 0.5) are
+ rounded upwards. This behaviour ensures that if an X% quantile is
+ requested, then at least the requested coverage
+ will be present in the central region, and no more than
+ the requested coverage will be present in the tails.
+ 
+
+ This behaviour can be changed so that the quantile functions are
+ rounded differently, or even return a real-valued result using <a class="link" href="../../../policy/pol_overview.html" title="Policy Overview">Policies</a>. It is
+ strongly recommended that you read the tutorial <a class="link" href="../../../policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
+ Quantiles of Discrete Distributions</a> before using the quantile
+ function on the geometric distribution. The <a class="link" href="../../../policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">reference
+ docs</a> describe how to change the rounding policy for these
+ distributions.
+ 
</td></tr>
</table></div>
+
+ 
<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.member_functions"></a><h5>
-<a name="id1006620"></a>
+<a name="id1114864"></a>
 <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="id1006636"></a>
+<a name="id1114879"></a>
 <a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.constructor">Constructor</a>
 </h6>
<pre class="programlisting">geometric_distribution(RealType p);
@@ -226,7 +231,7 @@
 1</code>.
 
<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.accessors"></a><h6>
-<a name="id1006715"></a>
+<a name="id1114958"></a>
 <a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.accessors">Accessors</a>
 </h6>
<pre class="programlisting">RealType success_fraction() const; // successes / trials (0 <= p <= 1)
@@ -253,7 +258,7 @@
 Binomial Distribution</a> for more discussion.
 
<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.lower_bound_on_success_fraction_parameter__emphasis_p__emphasis_"></a><h6>
-<a name="id1006823"></a>
+<a name="id1115066"></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
 Bound on success_fraction Parameter p</a>
 </h6>
@@ -308,7 +313,7 @@
 vol. 48, no3, 605-621</a>.
 
<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.upper_bound_on_success_fraction_parameter_p"></a><h6>
-<a name="id1007054"></a>
+<a name="id1115297"></a>
 <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>
@@ -363,7 +368,7 @@
 vol. 48, no3, 605-621</a>.
 
<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="id1007282"></a>
+<a name="id1115594"></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
 Number of Trials to Ensure at Least a Certain Number of Failures</a>
 </h6>
@@ -415,7 +420,7 @@
 probability of observing k failures or fewer.
 
<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="id1007520"></a>
+<a name="id1115832"></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
 Number of Trials to Ensure a Maximum Number of Failures or Less</a>
 </h6>
@@ -463,7 +468,7 @@
 probability of observing more than k failures.
 
<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.non_member_accessors"></a><h5>
-<a name="id1007756"></a>
+<a name="id1116068"></a>
 <a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -611,7 +616,7 @@
</table></div>
</div>
 <a name="math_toolkit.dist.dist_ref.dists.geometric_dist.accuracy"></a><h5>
-<a name="id1008266"></a>
+<a name="id1116578"></a>
 <a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.accuracy">Accuracy</a>
 </h5>

@@ -622,7 +627,7 @@
 for example to 10 decimal digits (from 16).
 
<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.implementation"></a><h5>
-<a name="id1009049"></a>
+<a name="id1116610"></a>
 <a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.implementation">Implementation</a>
 </h5>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist"></a><a class="link" href="hypergeometric_dist.html" title="Hypergeometric Distribution">Hypergeometric
- Distribution</a>
+<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist"></a><a class="link" href="hypergeometric_dist.html" title="Hypergeometric Distribution">
+ Hypergeometric Distribution</a>
</h5></div></div></div>


@@ -102,7 +102,7 @@
 <img src="../../../../../graphs/hypergeometric_pdf_2.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.member_functions"></a><h5>
-<a name="id1010037"></a>
+<a name="id1119992"></a>
 <a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -131,7 +131,7 @@
 from the population N.
 
<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.non_member_accessors"></a><h5>
-<a name="id1010216"></a>
+<a name="id1120171"></a>
 <a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -185,7 +185,7 @@
</td></tr>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.accuracy"></a><h5>
-<a name="id1010366"></a>
+<a name="id1120321"></a>
 <a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.accuracy">Accuracy</a>
 </h5>

@@ -211,7 +211,7 @@
 meaningless for N >= 1015.
 
<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.testing"></a><h5>
-<a name="id1010600"></a>
+<a name="id1120555"></a>
 <a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.testing">Testing</a>
 </h5>

@@ -223,7 +223,7 @@
 this implementation and NTL::RR.
 
<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.implementation"></a><h5>
-<a name="id1010624"></a>
+<a name="id1120579"></a>
 <a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.implementation">Implementation</a>
 </h5>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist"></a><a class="link" href="inverse_chi_squared_dist.html" title="Inverse Chi Squared Distribution">Inverse
- Chi Squared Distribution</a>
+<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist"></a><a class="link" href="inverse_chi_squared_dist.html" title="Inverse Chi Squared Distribution">
+ Inverse Chi Squared Distribution</a>
</h5></div></div></div>


@@ -198,7 +198,7 @@
 <img src="../../../../../graphs/inverse_chi_squared_cdf.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.member_functions"></a><h5>
-<a name="id1012241"></a>
+<a name="id1121606"></a>
 <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>
@@ -225,7 +225,7 @@
 Returns the scale ξ parameter of this distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.non_member_accessors"></a><h5>
-<a name="id1012413"></a>
+<a name="id1121778"></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
 Accessors</a>
 </h5>
@@ -255,7 +255,7 @@
 </td></tr>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.accuracy"></a><h5>
-<a name="id1012517"></a>
+<a name="id1121882"></a>
 <a class="link" href="inverse_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.accuracy">Accuracy</a>
 </h5>

@@ -271,7 +271,7 @@
 iteration is involved, as for the estimation of degrees of freedom.
 
<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.implementation"></a><h5>
-<a name="id1012558"></a>
+<a name="id1121923"></a>
 <a class="link" href="inverse_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.implementation">Implementation</a>
 </h5>

@@ -452,7 +452,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist.references"></a><h5>
-<a name="id1012887"></a>
+<a name="id1123130"></a>
 <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 type="1">

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist"></a><a class="link" href="inverse_gamma_dist.html" title="Inverse Gamma Distribution">Inverse
- Gamma Distribution</a>
+<a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist"></a><a class="link" href="inverse_gamma_dist.html" title="Inverse Gamma Distribution">
+ Inverse Gamma Distribution</a>
</h5></div></div></div>


@@ -130,7 +130,7 @@
 <img src="../../../../../graphs/inverse_gamma_cdf.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.member_functions"></a><h5>
-<a name="id1013468"></a>
+<a name="id1123711"></a>
 <a class="link" href="inverse_gamma_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -154,7 +154,7 @@
 Returns the β scale parameter of this inverse gamma distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.non_member_accessors"></a><h5>
-<a name="id1013605"></a>
+<a name="id1123848"></a>
 <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>
@@ -184,7 +184,7 @@
 </td></tr>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.accuracy"></a><h5>
-<a name="id1013711"></a>
+<a name="id1123955"></a>
 <a class="link" href="inverse_gamma_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.accuracy">Accuracy</a>
 </h5>

@@ -198,7 +198,7 @@
 >14 decimal digits accuracy for 64-bit double.
 
<a name="math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.implementation"></a><h5>
-<a name="id1013750"></a>
+<a name="id1123993"></a>
 <a class="link" href="inverse_gamma_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gamma_dist.implementation">Implementation</a>
 </h5>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist"></a><a class="link" href="inverse_gaussian_dist.html" title="Inverse Gaussian (or Inverse Normal) Distribution">Inverse
- Gaussian (or Inverse Normal) Distribution</a>
+<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist"></a><a class="link" href="inverse_gaussian_dist.html" title="Inverse Gaussian (or Inverse Normal) Distribution">
+ Inverse Gaussian (or Inverse Normal) Distribution</a>
</h5></div></div></div>


@@ -146,7 +146,7 @@
 the __wald_distrib (where mean μ is unity) is also provided.
 
<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.member_functions"></a><h5>
-<a name="id1016826"></a>
+<a name="id1124927"></a>
 <a class="link" href="inverse_gaussian_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -171,7 +171,7 @@
 Returns the scale λ parameter of this distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.non_member_accessors"></a><h5>
-<a name="id1016966"></a>
+<a name="id1125067"></a>
 <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>
@@ -201,7 +201,7 @@
 </td></tr>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.accuracy"></a><h5>
-<a name="id1017073"></a>
+<a name="id1125174"></a>
 <a class="link" href="inverse_gaussian_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.accuracy">Accuracy</a>
 </h5>

@@ -212,7 +212,7 @@
 to a few epsilon, >14 decimal digits accuracy for 64-bit double.
 
<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.implementation"></a><h5>
-<a name="id1017096"></a>
+<a name="id1125197"></a>
 <a class="link" href="inverse_gaussian_dist.html#math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.implementation">Implementation</a>
 </h5>

@@ -390,7 +390,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist.references"></a><h5>
-<a name="id1017391"></a>
+<a name="id1125831"></a>
 <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 type="1">

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.laplace_dist"></a><a class="link" href="laplace_dist.html" title="Laplace Distribution">Laplace
+<a name="math_toolkit.dist.dist_ref.dists.laplace_dist"></a><a class="link" href="laplace_dist.html" title="Laplace Distribution"> Laplace
 Distribution</a>
</h5></div></div></div>

@@ -81,7 +81,7 @@
 <img src="../../../../../graphs/laplace_pdf.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.member_functions"></a><h5>
-<a name="id1017976"></a>
+<a name="id1126416"></a>
 <a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -113,7 +113,7 @@
 Returns the scale parameter of this distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.non_member_accessors"></a><h5>
-<a name="id1018138"></a>
+<a name="id1126578"></a>
 <a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -133,7 +133,7 @@
 The domain of the random variable is [-∞,+∞].
 
<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.accuracy"></a><h5>
-<a name="id1018236"></a>
+<a name="id1126676"></a>
 <a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.accuracy">Accuracy</a>
 </h5>

@@ -141,7 +141,7 @@
 log and exp functions and as such should have very small errors.
 
<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.implementation"></a><h5>
-<a name="id1018255"></a>
+<a name="id1126695"></a>
 <a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.implementation">Implementation</a>
 </h5>

@@ -329,7 +329,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.references"></a><h5>
-<a name="id1018847"></a>
+<a name="id1127016"></a>
 <a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.references">References</a>
 </h5>
<div class="itemizedlist"><ul type="disc">

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.logistic_dist"></a><a class="link" href="logistic_dist.html" title="Logistic Distribution">Logistic
- Distribution</a>
+<a name="math_toolkit.dist.dist_ref.dists.logistic_dist"></a><a class="link" href="logistic_dist.html" title="Logistic Distribution">
+ Logistic Distribution</a>
</h5></div></div></div>


@@ -72,7 +72,7 @@
 <img src="../../../../../graphs/logistic_pdf.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.member_functions"></a><h5>
-<a name="id1019336"></a>
+<a name="id1127506"></a>
 <a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -98,7 +98,7 @@
 Returns the scale of this distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.non_member_accessors"></a><h5>
-<a name="id1019502"></a>
+<a name="id1127672"></a>
 <a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -128,7 +128,7 @@
 and +<a class="link" href="../../../main_overview/error_handling.html#overflow_error">overflow_error</a> respectively.
 
<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.accuracy"></a><h5>
-<a name="id1019652"></a>
+<a name="id1128935"></a>
 <a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.accuracy">Accuracy</a>
 </h5>

@@ -140,7 +140,7 @@
 error can be guarenteed.
 
<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.implementation"></a><h5>
-<a name="id1019707"></a>
+<a name="id1128990"></a>
 <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">

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist"></a><a class="link" href="lognormal_dist.html" title="Log Normal Distribution">Log
- Normal Distribution</a>
+<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist"></a><a class="link" href="lognormal_dist.html" title="Log Normal Distribution">
+ Log Normal Distribution</a>
</h5></div></div></div>


@@ -88,7 +88,7 @@
 <img src="../../../../../graphs/lognormal_pdf2.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.member_functions"></a><h5>
-<a name="id1020457"></a>
+<a name="id1129740"></a>
 <a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -121,7 +121,7 @@
 Returns the scale parameter of this distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.non_member_accessors"></a><h5>
-<a name="id1020617"></a>
+<a name="id1129900"></a>
 <a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -141,7 +141,7 @@
 The domain of the random variable is [0,+∞].
 
<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.accuracy"></a><h5>
-<a name="id1020716"></a>
+<a name="id1130000"></a>
 <a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.accuracy">Accuracy</a>
 </h5>

@@ -150,7 +150,7 @@
 function</a>, and as such should have very low error rates.
 
<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.implementation"></a><h5>
-<a name="id1020744"></a>
+<a name="id1130027"></a>
 <a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.implementation">Implementation</a>
 </h5>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist"></a><a class="link" href="nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral
+<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist"></a><a class="link" href="nc_beta_dist.html" title="Noncentral Beta Distribution"> Noncentral
 Beta Distribution</a>
</h5></div></div></div>

@@ -96,7 +96,7 @@
 <img src="../../../../../graphs/nc_beta_pdf.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.member_functions"></a><h5>
-<a name="id1025394"></a>
+<a name="id1135287"></a>
 <a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -128,7 +128,7 @@
 was constructed.
 
<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.non_member_accessors"></a><h5>
-<a name="id1026823"></a>
+<a name="id1135473"></a>
 <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>
@@ -156,7 +156,7 @@
 The domain of the random variable is [0, 1].
 
<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.accuracy"></a><h5>
-<a name="id1026932"></a>
+<a name="id1135582"></a>
 <a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.accuracy">Accuracy</a>
 </h5>

@@ -299,7 +299,7 @@
 functions are broadly similar.
 
<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.tests"></a><h5>
-<a name="id1027175"></a>
+<a name="id1135825"></a>
 <a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.tests">Tests</a>
 </h5>

@@ -311,7 +311,7 @@
 tests.
 
<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.implementation"></a><h5>
-<a name="id1027199"></a>
+<a name="id1135849"></a>
 <a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.implementation">Implementation</a>
 </h5>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist"></a><a class="link" href="nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral
- Chi-Squared Distribution</a>
+<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist"></a><a class="link" href="nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">
+ Noncentral Chi-Squared Distribution</a>
</h5></div></div></div>


@@ -110,7 +110,7 @@
 <img src="../../../../../graphs/nccs_pdf.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.member_functions"></a><h5>
-<a name="id1028218"></a>
+<a name="id1137999"></a>
 <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>
@@ -183,7 +183,7 @@
 == q</code>.
 
<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.non_member_accessors"></a><h5>
-<a name="id1029983"></a>
+<a name="id1138900"></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
 Accessors</a>
 </h5>
@@ -203,7 +203,7 @@
 The domain of the random variable is [0, +∞].
 
<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.examples"></a><h5>
-<a name="id1030083"></a>
+<a name="id1138999"></a>
 <a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.examples">Examples</a>
 </h5>

@@ -211,7 +211,7 @@
 example</a> for the noncentral chi-squared distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.accuracy"></a><h5>
-<a name="id1030111"></a>
+<a name="id1139027"></a>
 <a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.accuracy">Accuracy</a>
 </h5>

@@ -359,7 +359,7 @@
 produce an accuracy greater than the square root of the machine epsilon.
 
<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.tests"></a><h5>
-<a name="id1030371"></a>
+<a name="id1139287"></a>
 <a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.tests">Tests</a>
 </h5>

@@ -373,7 +373,7 @@
 to at least 50 decimal digits - and is the used for our accuracy tests.
 
<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.implementation"></a><h5>
-<a name="id1030390"></a>
+<a name="id1139307"></a>
 <a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.implementation">Implementation</a>
 </h5>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist"></a><a class="link" href="nc_f_dist.html" title="Noncentral F Distribution">Noncentral
+<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist"></a><a class="link" href="nc_f_dist.html" title="Noncentral F Distribution"> Noncentral
 F Distribution</a>
</h5></div></div></div>

@@ -95,7 +95,7 @@
 <img src="../../../../../graphs/nc_f_pdf.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.member_functions"></a><h5>
-<a name="id1031243"></a>
+<a name="id1141608"></a>
 <a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -127,7 +127,7 @@
 which this object was constructed.
 
<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.non_member_accessors"></a><h5>
-<a name="id1031432"></a>
+<a name="id1141796"></a>
 <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>
@@ -147,7 +147,7 @@
 The domain of the random variable is [0, +∞].
 
<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.accuracy"></a><h5>
-<a name="id1031531"></a>
+<a name="id1141896"></a>
 <a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.accuracy">Accuracy</a>
 </h5>

@@ -155,7 +155,7 @@
 Beta Distribution</a>: refer to that distribution for accuracy data.
 
<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.tests"></a><h5>
-<a name="id1031555"></a>
+<a name="id1141920"></a>
 <a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.tests">Tests</a>
 </h5>

@@ -164,7 +164,7 @@
 Math library statistical package</a> and its pbeta and dbeta functions.
 
<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.implementation"></a><h5>
-<a name="id1031579"></a>
+<a name="id1141944"></a>
 <a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.implementation">Implementation</a>
 </h5>

@@ -234,6 +234,8 @@
 
 y = x * v1 / v2
 
+ 
+ 
 </td>
</tr>
<tr>
@@ -256,6 +258,8 @@
 
 y = x * v1 / v2
 
+ 
+ 
 </td>
</tr>
<tr>
@@ -286,6 +290,8 @@
 
 is the noncentral beta quantile.
 
+ 
+ 
 </td>
</tr>
<tr>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist"></a><a class="link" href="nc_t_dist.html" title="Noncentral T Distribution">Noncentral
+<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist"></a><a class="link" href="nc_t_dist.html" title="Noncentral T Distribution"> Noncentral
 T Distribution</a>
</h5></div></div></div>

@@ -85,7 +85,7 @@
 <img src="../../../../../graphs/nc_t_pdf.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.member_functions"></a><h5>
-<a name="id1033898"></a>
+<a name="id1142839"></a>
 <a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -111,7 +111,7 @@
 which this object was constructed.
 
<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.non_member_accessors"></a><h5>
-<a name="id1034037"></a>
+<a name="id1142978"></a>
 <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>
@@ -131,7 +131,7 @@
 The domain of the random variable is [-∞, +∞].
 
<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.accuracy"></a><h5>
-<a name="id1034137"></a>
+<a name="id1143078"></a>
 <a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.accuracy">Accuracy</a>
 </h5>

@@ -255,7 +255,7 @@
 epsilon.
 
<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.tests"></a><h5>
-<a name="id1034337"></a>
+<a name="id1143289"></a>
 <a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.tests">Tests</a>
 </h5>

@@ -270,7 +270,7 @@
 least 50 decimal places.
 
<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.implementation"></a><h5>
-<a name="id1034356"></a>
+<a name="id1143308"></a>
 <a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.implementation">Implementation</a>
 </h5>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist"></a><a class="link" href="negative_binomial_dist.html" title="Negative Binomial Distribution">Negative
- Binomial Distribution</a>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist"></a><a class="link" href="negative_binomial_dist.html" title="Negative Binomial Distribution">
+ Negative Binomial Distribution</a>
</h5></div></div></div>


@@ -123,7 +123,7 @@
 <img src="../../../../../graphs/negative_binomial_pdf_2.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.related_distributions"></a><h5>
-<a name="id1021920"></a>
+<a name="id1131264"></a>
 <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.related_distributions">Related
 Distributions</a>
 </h5>
@@ -160,6 +160,8 @@

 poisson(λ) = lim r → ∞   negative_binomial(r, r / (λ + r)))
 
+
+ 
<div class="caution"><table border="0" summary="Caution">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../../../doc/src/images/caution.png"></td>
@@ -167,40 +169,43 @@
</tr>
<tr><td align="left" valign="top">

- The Negative Binomial distribution is a discrete distribution: internally,
- functions like the <code class="computeroutput">cdf</code>
- and <code class="computeroutput">pdf</code> are treated
- "as if" they are continuous functions, but in reality the
- results returned from these functions only have meaning if an integer
- value is provided for the random variate argument.
- 
-
- The quantile function will by default return an integer result that
- has been rounded outwards. That is to say lower
- quantiles (where the probability is less than 0.5) are rounded downward,
- and upper quantiles (where the probability is greater than 0.5) are
- rounded upwards. This behaviour ensures that if an X% quantile is requested,
- then at least the requested coverage will be present
- in the central region, and no more than the requested
- coverage will be present in the tails.
- 
-
- This behaviour can be changed so that the quantile functions are rounded
- differently, or even return a real-valued result using <a class="link" href="../../../policy/pol_overview.html" title="Policy Overview">Policies</a>.
- It is strongly recommended that you read the tutorial <a class="link" href="../../../policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
- Quantiles of Discrete Distributions</a> before using the quantile
- function on the Negative Binomial distribution. The <a class="link" href="../../../policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">reference
- docs</a> describe how to change the rounding policy for these distributions.
- 
+ The Negative Binomial distribution is a discrete distribution: internally,
+ functions like the <code class="computeroutput">cdf</code>
+ and <code class="computeroutput">pdf</code> are treated
+ "as if" they are continuous functions, but in reality the
+ results returned from these functions only have meaning if an integer
+ value is provided for the random variate argument.
+ 
+
+ The quantile function will by default return an integer result that
+ has been rounded outwards. That is to say lower
+ quantiles (where the probability is less than 0.5) are rounded downward,
+ and upper quantiles (where the probability is greater than 0.5) are
+ rounded upwards. This behaviour ensures that if an X% quantile is
+ requested, then at least the requested coverage
+ will be present in the central region, and no more than
+ the requested coverage will be present in the tails.
+ 
+
+ This behaviour can be changed so that the quantile functions are
+ rounded differently, or even return a real-valued result using <a class="link" href="../../../policy/pol_overview.html" title="Policy Overview">Policies</a>. It is
+ strongly recommended that you read the tutorial <a class="link" href="../../../policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
+ Quantiles of Discrete Distributions</a> before using the quantile
+ function on the Negative Binomial distribution. The <a class="link" href="../../../policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">reference
+ docs</a> describe how to change the rounding policy for these
+ distributions.
+ 
</td></tr>
</table></div>
+
+ 
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.member_functions"></a><h5>
-<a name="id1022028"></a>
+<a name="id1131375"></a>
 <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="id1022041"></a>
+<a name="id1131388"></a>
 <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.construct">Construct</a>
 </h6>
<pre class="programlisting">negative_binomial_distribution(RealType r, RealType p);
@@ -216,7 +221,7 @@
 <= 1</code>.
 
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accessors"></a><h6>
-<a name="id1022150"></a>
+<a name="id1131497"></a>
 <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accessors">Accessors</a>
 </h6>
<pre class="programlisting">RealType success_fraction() const; // successes / trials (0 <= p <= 1)
@@ -237,7 +242,7 @@
 Distribution</a> for more discussion.
 
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.lower_bound_on_parameter_p"></a><h6>
-<a name="id1022244"></a>
+<a name="id1131591"></a>
 <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>
@@ -298,7 +303,7 @@
 vol. 48, no3, 605-621</a>.
 
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.upper_bound_on_parameter_p"></a><h6>
-<a name="id1022511"></a>
+<a name="id1131858"></a>
 <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>
@@ -358,7 +363,7 @@
 vol. 48, no3, 605-621</a>.
 
<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="id1022775"></a>
+<a name="id1132122"></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
 Number of Trials to Ensure at Least a Certain Number of Failures</a>
 </h6>
@@ -409,7 +414,7 @@
 probability of observing k failures or fewer.
 
<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="id1023240"></a>
+<a name="id1132347"></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
 Number of Trials to Ensure a Maximum Number of Failures or Less</a>
 </h6>
@@ -457,7 +462,7 @@
 probability of observing more than k failures.
 
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.non_member_accessors"></a><h5>
-<a name="id1023472"></a>
+<a name="id1132578"></a>
 <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>
@@ -606,7 +611,7 @@
</table></div>
</div>
 <a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accuracy"></a><h5>
-<a name="id1023985"></a>
+<a name="id1133092"></a>
 <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accuracy">Accuracy</a>
 </h5>

@@ -616,7 +621,7 @@
 please refer to these functions for information on accuracy.
 
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.implementation"></a><h5>
-<a name="id1024012"></a>
+<a name="id1133118"></a>
 <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.implementation">Implementation</a>
 </h5>

@@ -827,6 +832,8 @@
 
 </td>
<td>
+ 
+ 
 </td>
</tr>
<tr>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.normal_dist"></a><a class="link" href="normal_dist.html" title="Normal (Gaussian) Distribution">Normal
+<a name="math_toolkit.dist.dist_ref.dists.normal_dist"></a><a class="link" href="normal_dist.html" title="Normal (Gaussian) Distribution"> Normal
 (Gaussian) Distribution</a>
</h5></div></div></div>

@@ -79,7 +79,7 @@
 <img src="../../../../../graphs/normal_pdf.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.normal_dist.member_functions"></a><h5>
-<a name="id1035070"></a>
+<a name="id1144022"></a>
 <a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -109,7 +109,7 @@
 be used generically).
 
<a name="math_toolkit.dist.dist_ref.dists.normal_dist.non_member_accessors"></a><h5>
-<a name="id1035266"></a>
+<a name="id1144218"></a>
 <a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -131,7 +131,7 @@
 and complement cdf -∞ = 1 and +∞ = 0, if RealType permits.
 
<a name="math_toolkit.dist.dist_ref.dists.normal_dist.accuracy"></a><h5>
-<a name="id1035363"></a>
+<a name="id1144315"></a>
 <a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.accuracy">Accuracy</a>
 </h5>

@@ -139,7 +139,7 @@
 function</a>, and as such should have very low error rates.
 
<a name="math_toolkit.dist.dist_ref.dists.normal_dist.implementation"></a><h5>
-<a name="id1035388"></a>
+<a name="id1144340"></a>
 <a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.implementation">Implementation</a>
 </h5>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.pareto"></a><a class="link" href="pareto.html" title="Pareto Distribution">Pareto Distribution</a>
+<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>


@@ -86,12 +87,12 @@
 <img src="../../../../../graphs/pareto_pdf2.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.pareto.related_distributions"></a><h5>
-<a name="id1038528"></a>
+<a name="id1145124"></a>
 <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="id1038546"></a>
+<a name="id1145142"></a>
 <a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.member_functions">Member
 Functions</a>
 </h5>
@@ -117,7 +118,7 @@
 Returns the shape parameter of this distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.pareto.non_member_accessors"></a><h5>
-<a name="id1038714"></a>
+<a name="id1145310"></a>
 <a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -137,7 +138,7 @@
 The supported domain of the random variable is [scale, ∞].
 
<a name="math_toolkit.dist.dist_ref.dists.pareto.accuracy"></a><h5>
-<a name="id1038813"></a>
+<a name="id1145410"></a>
 <a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.accuracy">Accuracy</a>
 </h5>

@@ -150,7 +151,7 @@
 zero) see also <a class="link" href="../../stat_tut/overview/complements.html#why_complements">why complements?</a>.
 
<a name="math_toolkit.dist.dist_ref.dists.pareto.implementation"></a><h5>
-<a name="id1038850"></a>
+<a name="id1146909"></a>
 <a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.implementation">Implementation</a>
 </h5>

@@ -318,7 +319,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.pareto.references"></a><h5>
-<a name="id1039158"></a>
+<a name="id1147216"></a>
 <a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.references">References</a>
 </h5>
<div class="itemizedlist"><ul type="disc">

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.poisson_dist"></a><a class="link" href="poisson_dist.html" title="Poisson Distribution">Poisson
+<a name="math_toolkit.dist.dist_ref.dists.poisson_dist"></a><a class="link" href="poisson_dist.html" title="Poisson Distribution"> Poisson
 Distribution</a>
</h5></div></div></div>

@@ -82,6 +82,8 @@

 <img src="../../../../../graphs/poisson_pdf_1.png" align="middle">
 
+
+ 
<div class="caution"><table border="0" summary="Caution">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../../../doc/src/images/caution.png"></td>
@@ -89,34 +91,38 @@
</tr>
<tr><td align="left" valign="top">

- The Poisson distribution is a discrete distribution: internally, functions
- like the <code class="computeroutput">cdf</code> and <code class="computeroutput">pdf</code> are treated "as if"
- they are continuous functions, but in reality the results returned
- from these functions only have meaning if an integer value is provided
- for the random variate argument.
- 
-
- The quantile function will by default return an integer result that
- has been rounded outwards. That is to say lower
- quantiles (where the probability is less than 0.5) are rounded downward,
- and upper quantiles (where the probability is greater than 0.5) are
- rounded upwards. This behaviour ensures that if an X% quantile is requested,
- then at least the requested coverage will be present
- in the central region, and no more than the requested
- coverage will be present in the tails.
- 
-
- This behaviour can be changed so that the quantile functions are rounded
- differently, or even return a real-valued result using <a class="link" href="../../../policy/pol_overview.html" title="Policy Overview">Policies</a>.
- It is strongly recommended that you read the tutorial <a class="link" href="../../../policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
- Quantiles of Discrete Distributions</a> before using the quantile
- function on the Poisson distribution. The <a class="link" href="../../../policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">reference
- docs</a> describe how to change the rounding policy for these distributions.
- 
+ The Poisson distribution is a discrete distribution: internally,
+ functions like the <code class="computeroutput">cdf</code>
+ and <code class="computeroutput">pdf</code> are treated
+ "as if" they are continuous functions, but in reality the
+ results returned from these functions only have meaning if an integer
+ value is provided for the random variate argument.
+ 
+
+ The quantile function will by default return an integer result that
+ has been rounded outwards. That is to say lower
+ quantiles (where the probability is less than 0.5) are rounded downward,
+ and upper quantiles (where the probability is greater than 0.5) are
+ rounded upwards. This behaviour ensures that if an X% quantile is
+ requested, then at least the requested coverage
+ will be present in the central region, and no more than
+ the requested coverage will be present in the tails.
+ 
+
+ This behaviour can be changed so that the quantile functions are
+ rounded differently, or even return a real-valued result using <a class="link" href="../../../policy/pol_overview.html" title="Policy Overview">Policies</a>. It is
+ strongly recommended that you read the tutorial <a class="link" href="../../../policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
+ Quantiles of Discrete Distributions</a> before using the quantile
+ function on the Poisson distribution. The <a class="link" href="../../../policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">reference
+ docs</a> describe how to change the rounding policy for these
+ distributions.
+ 
</td></tr>
</table></div>
+
+ 
<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.member_functions"></a><h5>
-<a name="id1039688"></a>
+<a name="id1147749"></a>
 <a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -131,7 +137,7 @@
 Returns the mean of this distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.non_member_accessors"></a><h5>
-<a name="id1039777"></a>
+<a name="id1147838"></a>
 <a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -151,7 +157,7 @@
 The domain of the random variable is [0, ∞].
 
<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.accuracy"></a><h5>
-<a name="id1039874"></a>
+<a name="id1147935"></a>
 <a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.accuracy">Accuracy</a>
 </h5>

@@ -165,7 +171,7 @@
 using an iterative method with a lower tolerance to avoid excessive computation.
 
<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.implementation"></a><h5>
-<a name="id1039903"></a>
+<a name="id1147964"></a>
 <a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.implementation">Implementation</a>
 </h5>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.rayleigh"></a><a class="link" href="rayleigh.html" title="Rayleigh Distribution">Rayleigh
+<a name="math_toolkit.dist.dist_ref.dists.rayleigh"></a><a class="link" href="rayleigh.html" title="Rayleigh Distribution"> Rayleigh
 Distribution</a>
</h5></div></div></div>

@@ -86,7 +86,7 @@
 <img src="../../../../../graphs/rayleigh_cdf.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.rayleigh.related_distributions"></a><h5>
-<a name="id1040645"></a>
+<a name="id1148685"></a>
 <a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.related_distributions">Related
 distributions</a>
 </h5>
@@ -102,7 +102,7 @@
 distribution</a>.
 
<a name="math_toolkit.dist.dist_ref.dists.rayleigh.member_functions"></a><h5>
-<a name="id1040696"></a>
+<a name="id1148736"></a>
 <a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.member_functions">Member
 Functions</a>
 </h5>
@@ -121,7 +121,7 @@
 Returns the sigma parameter of this distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.rayleigh.non_member_accessors"></a><h5>
-<a name="id1040799"></a>
+<a name="id1148840"></a>
 <a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -141,7 +141,7 @@
 The domain of the random variable is [0, max_value].
 
<a name="math_toolkit.dist.dist_ref.dists.rayleigh.accuracy"></a><h5>
-<a name="id1040899"></a>
+<a name="id1148939"></a>
 <a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.accuracy">Accuracy</a>
 </h5>

@@ -151,7 +151,7 @@
 using NTL RR type with 150-bit accuracy, about 50 decimal digits.
 
<a name="math_toolkit.dist.dist_ref.dists.rayleigh.implementation"></a><h5>
-<a name="id1040933"></a>
+<a name="id1148973"></a>
 <a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.implementation">Implementation</a>
 </h5>

@@ -320,7 +320,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.rayleigh.references"></a><h5>
-<a name="id1041269"></a>
+<a name="id1149378"></a>
 <a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.references">References</a>
 </h5>
<div class="itemizedlist"><ul type="disc">

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.students_t_dist"></a><a class="link" href="students_t_dist.html" title="Students t Distribution">Students
- t Distribution</a>
+<a name="math_toolkit.dist.dist_ref.dists.students_t_dist"></a><a class="link" href="students_t_dist.html" title="Students t Distribution">
+ Students t Distribution</a>
</h5></div></div></div>


@@ -97,7 +97,7 @@
 <img src="../../../../../graphs/students_t_pdf.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.member_functions"></a><h5>
-<a name="id1041849"></a>
+<a name="id1149958"></a>
 <a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -174,7 +174,7 @@
 Engineering Statistics Handbook</a>.
 
<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.non_member_accessors"></a><h5>
-<a name="id1042140"></a>
+<a name="id1150249"></a>
 <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>
@@ -194,7 +194,7 @@
 The domain of the random variable is [-∞, +∞].
 
<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.examples"></a><h5>
-<a name="id1042239"></a>
+<a name="id1150348"></a>
 <a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.examples">Examples</a>
 </h5>

@@ -202,7 +202,7 @@
 are available illustrating the use of the Student's t distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.accuracy"></a><h5>
-<a name="id1043170"></a>
+<a name="id1150375"></a>
 <a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.accuracy">Accuracy</a>
 </h5>

@@ -211,7 +211,7 @@
 inverses</a>, refer to accuracy data on those functions for more information.
 
<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.implementation"></a><h5>
-<a name="id1043201"></a>
+<a name="id1150406"></a>
 <a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.implementation">Implementation</a>
 </h5>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.triangular_dist"></a><a class="link" href="triangular_dist.html" title="Triangular Distribution">Triangular
- Distribution</a>
+<a name="math_toolkit.dist.dist_ref.dists.triangular_dist"></a><a class="link" href="triangular_dist.html" title="Triangular Distribution">
+ Triangular Distribution</a>
</h5></div></div></div>


@@ -128,7 +128,7 @@
 <img src="../../../../../graphs/triangular_cdf.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.member_functions"></a><h5>
-<a name="id1044231"></a>
+<a name="id1152665"></a>
 <a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -163,7 +163,7 @@
 (default+1).
 
<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.non_member_accessors"></a><h5>
-<a name="id1044449"></a>
+<a name="id1152883"></a>
 <a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -184,7 +184,7 @@
 range is lower <= x <= upper.
 
<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.accuracy"></a><h5>
-<a name="id1044549"></a>
+<a name="id1152983"></a>
 <a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.accuracy">Accuracy</a>
 </h5>

@@ -193,7 +193,7 @@
 with arguments nearing the extremes of zero and unity.
 
<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.implementation"></a><h5>
-<a name="id1044570"></a>
+<a name="id1153004"></a>
 <a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.implementation">Implementation</a>
 </h5>

@@ -378,7 +378,7 @@
 Calculate and plot probability distributions</a>
 
<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.references"></a><h5>
-<a name="id1044911"></a>
+<a name="id1153345"></a>
 <a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.references">References</a>
 </h5>
<div class="itemizedlist"><ul type="disc">

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.uniform_dist"></a><a class="link" href="uniform_dist.html" title="Uniform Distribution">Uniform
+<a name="math_toolkit.dist.dist_ref.dists.uniform_dist"></a><a class="link" href="uniform_dist.html" title="Uniform Distribution"> Uniform
 Distribution</a>
</h5></div></div></div>

@@ -117,7 +117,7 @@
 <img src="../../../../../graphs/uniform_cdf.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.member_functions"></a><h5>
-<a name="id1047037"></a>
+<a name="id1154024"></a>
 <a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -144,7 +144,7 @@
 Returns the upper parameter of this distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.non_member_accessors"></a><h5>
-<a name="id1047203"></a>
+<a name="id1154190"></a>
 <a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -165,7 +165,7 @@
 range is only lower <= x <= upper.
 
<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.accuracy"></a><h5>
-<a name="id1047307"></a>
+<a name="id1154294"></a>
 <a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.accuracy">Accuracy</a>
 </h5>

@@ -173,7 +173,7 @@
 and so should have errors within an epsilon or two.
 
<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.implementation"></a><h5>
-<a name="id1047327"></a>
+<a name="id1154314"></a>
 <a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.implementation">Implementation</a>
 </h5>

@@ -337,7 +337,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.references"></a><h5>
-<a name="id1047605"></a>
+<a name="id1154592"></a>
 <a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.references">References</a>
 </h5>
<div class="itemizedlist"><ul type="disc">

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.dist_ref.dists.weibull_dist"></a><a class="link" href="weibull_dist.html" title="Weibull Distribution">Weibull
+<a name="math_toolkit.dist.dist_ref.dists.weibull_dist"></a><a class="link" href="weibull_dist.html" title="Weibull Distribution"> Weibull
 Distribution</a>
</h5></div></div></div>

@@ -100,7 +100,7 @@
 <img src="../../../../../graphs/weibull_pdf2.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.related_distributions"></a><h5>
-<a name="id1048164"></a>
+<a name="id1155425"></a>
 <a class="link" href="weibull_dist.html#math_toolkit.dist.dist_ref.dists.weibull_dist.related_distributions">Related
 distributions</a>
 </h5>
@@ -114,7 +114,7 @@
 Distributions, Theory and Applications Samuel Kotz & Saralees Nadarajah</a>.
 
<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.member_functions"></a><h5>
-<a name="id1048203"></a>
+<a name="id1155463"></a>
 <a class="link" href="weibull_dist.html#math_toolkit.dist.dist_ref.dists.weibull_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -140,7 +140,7 @@
 Returns the scale parameter of this distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.non_member_accessors"></a><h5>
-<a name="id1048359"></a>
+<a name="id1155619"></a>
 <a class="link" href="weibull_dist.html#math_toolkit.dist.dist_ref.dists.weibull_dist.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -160,7 +160,7 @@
 The domain of the random variable is [0, ∞].
 
<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.accuracy"></a><h5>
-<a name="id1048456"></a>
+<a name="id1155716"></a>
 <a class="link" href="weibull_dist.html#math_toolkit.dist.dist_ref.dists.weibull_dist.accuracy">Accuracy</a>
 </h5>

@@ -170,7 +170,7 @@
 as such should have very low error rates.
 
<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.implementation"></a><h5>
-<a name="id1048499"></a>
+<a name="id1155760"></a>
 <a class="link" href="weibull_dist.html#math_toolkit.dist.dist_ref.dists.weibull_dist.implementation">Implementation</a>
 </h5>

@@ -337,7 +337,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.weibull_dist.references"></a><h5>
-<a name="id1048831"></a>
+<a name="id1156092"></a>
 <a class="link" href="weibull_dist.html#math_toolkit.dist.dist_ref.dists.weibull_dist.references">References</a>
 </h5>
<div class="itemizedlist"><ul type="disc">

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h4 class="title">
-<a name="math_toolkit.dist.dist_ref.nmp"></a><a class="link" href="nmp.html" title="Non-Member Properties">Non-Member Properties</a>
+<a name="math_toolkit.dist.dist_ref.nmp"></a><a class="link" href="nmp.html" title="Non-Member Properties"> Non-Member Properties</a>
</h4></div></div></div>

 Properties that are common to all distributions are accessed via non-member
@@ -37,7 +37,7 @@
 the function you want if you already know its name.
 
<a name="function_index"></a><a name="math_toolkit.dist.dist_ref.nmp.function_index"></a><h5>
-<a name="id978145"></a>
+<a name="id1087551"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.function_index">Function
 Index</a>
 </h5>
@@ -95,7 +95,7 @@
 </li>
</ul></div>
<a name="concept_index"></a><a name="math_toolkit.dist.dist_ref.nmp.conceptual_index"></a><h5>
-<a name="id978369"></a>
+<a name="id1087776"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.conceptual_index">Conceptual
 Index</a>
 </h5>
@@ -182,7 +182,7 @@
 </li>
</ul></div>
<a name="math.dist.cdf"></a><a name="math_toolkit.dist.dist_ref.nmp.cumulative_distribution_function"></a><h5>
-<a name="id978705"></a>
+<a name="id1088152"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.cumulative_distribution_function">Cumulative
 Distribution Function</a>
 </h5>
@@ -206,7 +206,7 @@
 <img src="../../../../graphs/cdf.png" alt="cdf">
 
<a name="math.dist.ccdf"></a><a name="math_toolkit.dist.dist_ref.nmp.complement_of_the_cumulative_distribution_function"></a><h5>
-<a name="id978875"></a>
+<a name="id1088323"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.complement_of_the_cumulative_distribution_function">Complement
 of the Cumulative Distribution Function</a>
 </h5>
@@ -247,7 +247,7 @@
 complement is useful and when it should be used.
 
<a name="math.dist.hazard"></a><a name="math_toolkit.dist.dist_ref.nmp.hazard_function"></a><h5>
-<a name="id979165"></a>
+<a name="id1088612"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.hazard_function">Hazard Function</a>
 </h5>
<pre class="programlisting">template <class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
@@ -275,7 +275,7 @@
 </td></tr>
</table></div>
<a name="math.dist.chf"></a><a name="math_toolkit.dist.dist_ref.nmp.cumulative_hazard_function"></a><h5>
-<a name="id979347"></a>
+<a name="id1088794"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.cumulative_hazard_function">Cumulative
 Hazard Function</a>
 </h5>
@@ -303,7 +303,7 @@
 </td></tr>
</table></div>
<a name="math.dist.mean"></a><a name="math_toolkit.dist.dist_ref.nmp.mean"></a><h5>
-<a name="id979529"></a>
+<a name="id1088977"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.mean">mean</a>
 </h5>
<pre class="programlisting">template<class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
@@ -318,7 +318,7 @@
 distribution).
 
<a name="math.dist.median"></a><a name="math_toolkit.dist.dist_ref.nmp.median"></a><h5>
-<a name="id979647"></a>
+<a name="id1089094"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.median">median</a>
 </h5>
<pre class="programlisting">template<class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
@@ -328,7 +328,7 @@
 Returns the median of the distribution dist.
 
<a name="math.dist.mode"></a><a name="math_toolkit.dist.dist_ref.nmp.mode"></a><h5>
-<a name="id979756"></a>
+<a name="id1089203"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.mode">mode</a>
 </h5>
<pre class="programlisting">template<class RealType, <a class="link" href="../../policy.html" title="Policies">Policy</a>>
@@ -342,7 +342,7 @@
 if the distribution does not have a defined mode.
 
<a name="math.dist.pdf"></a><a name="math_toolkit.dist.dist_ref.nmp.probability_density_function"></a><h5>
-<a name="id980979"></a>
+<a name="id1089319"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.probability_density_function">Probability
 Density Function</a>
 </h5>
@@ -371,7 +371,7 @@
 <img src="../../../../graphs/pdf.png" alt="pdf">
 
<a name="math.dist.range"></a><a name="math_toolkit.dist.dist_ref.nmp.range"></a><h5>
-<a name="id981148"></a>
+<a name="id1089488"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.range">Range</a>
 </h5>
<pre class="programlisting">template<class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
@@ -381,7 +381,7 @@
 Returns the valid range of the random variable over distribution dist.
 
<a name="math.dist.quantile"></a><a name="math_toolkit.dist.dist_ref.nmp.quantile"></a><h5>
-<a name="id981284"></a>
+<a name="id1089623"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.quantile">Quantile</a>
 </h5>
<pre class="programlisting">template <class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
@@ -411,7 +411,7 @@
 <img src="../../../../graphs/quantile.png" alt="quantile">
 
<a name="math.dist.quantile_c"></a><a name="math_toolkit.dist.dist_ref.nmp.quantile_from_the_complement_of_the_probability_"></a><h5>
-<a name="id981511"></a>
+<a name="id1089850"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.quantile_from_the_complement_of_the_probability_">Quantile
 from the complement of the probability.</a>
 </h5>
@@ -457,7 +457,7 @@
 <img src="../../../../graphs/survival_inv.png" alt="survival_inv">
 
<a name="math.dist.sd"></a><a name="math_toolkit.dist.dist_ref.nmp.standard_deviation"></a><h5>
-<a name="id981852"></a>
+<a name="id1090191"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.standard_deviation">Standard
 Deviation</a>
 </h5>
@@ -472,7 +472,7 @@
 if the distribution does not have a defined standard deviation.
 
<a name="math.dist.support"></a><a name="math_toolkit.dist.dist_ref.nmp.support"></a><h5>
-<a name="id981972"></a>
+<a name="id1093588"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.support">support</a>
 </h5>
<pre class="programlisting">template<class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
@@ -489,7 +489,7 @@
 where the pdf is zero, and the cdf zero or unity.
 
<a name="math.dist.variance"></a><a name="math_toolkit.dist.dist_ref.nmp.variance"></a><h5>
-<a name="id982116"></a>
+<a name="id1093732"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.variance">Variance</a>
 </h5>
<pre class="programlisting">template <class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
@@ -503,7 +503,7 @@
 if the distribution does not have a defined variance.
 
<a name="math.dist.skewness"></a><a name="math_toolkit.dist.dist_ref.nmp.skewness"></a><h5>
-<a name="id982234"></a>
+<a name="id1093851"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.skewness">Skewness</a>
 </h5>
<pre class="programlisting">template <class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
@@ -517,7 +517,7 @@
 if the distribution does not have a defined skewness.
 
<a name="math.dist.kurtosis"></a><a name="math_toolkit.dist.dist_ref.nmp.kurtosis"></a><h5>
-<a name="id982353"></a>
+<a name="id1093970"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.kurtosis">Kurtosis</a>
 </h5>
<pre class="programlisting">template <class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
@@ -559,7 +559,7 @@
 'Proper' kurtosis can have a value from zero to + infinity.
 
<a name="math.dist.kurtosis_excess"></a><a name="math_toolkit.dist.dist_ref.nmp.kurtosis_excess"></a><h5>
-<a name="id982561"></a>
+<a name="id1094178"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.kurtosis_excess">Kurtosis
 excess</a>
 </h5>
@@ -594,7 +594,7 @@
 The kurtosis excess of a normal distribution is zero.
 
<a name="cdfPQ"></a><a name="math_toolkit.dist.dist_ref.nmp.p_and_q"></a><h5>
-<a name="id982747"></a>
+<a name="id1094364"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.p_and_q">P and Q</a>
 </h5>

@@ -604,7 +604,7 @@
 returned by these functions.
 
<a name="percent"></a><a name="math_toolkit.dist.dist_ref.nmp.percent_point_function_or_percentile"></a><h5>
-<a name="id982777"></a>
+<a name="id1094394"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.percent_point_function_or_percentile">Percent
 Point Function or Percentile</a>
 </h5>
@@ -613,7 +613,7 @@
 the <a class="link" href="nmp.html#math.dist.quantile">Quantile</a>.
 
<a name="cdf_inv"></a><a name="math_toolkit.dist.dist_ref.nmp.inverse_cdf_function_"></a><h5>
-<a name="id982802"></a>
+<a name="id1094419"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.inverse_cdf_function_">Inverse
 CDF Function.</a>
 </h5>
@@ -622,7 +622,7 @@
 <a class="link" href="nmp.html#math.dist.quantile">Quantile</a>.
 
<a name="survival_inv"></a><a name="math_toolkit.dist.dist_ref.nmp.inverse_survival_function_"></a><h5>
-<a name="id982830"></a>
+<a name="id1094446"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.inverse_survival_function_">Inverse
 Survival Function.</a>
 </h5>
@@ -630,7 +630,7 @@
 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>.
 
<a name="pmf"></a><a name="math_toolkit.dist.dist_ref.nmp.probability_mass_function"></a><h5>
-<a name="id982860"></a>
+<a name="id1094476"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.probability_mass_function">Probability
 Mass Function</a>
 </h5>
@@ -644,7 +644,7 @@
 applies to continuous distributions.
 
<a name="lower_critical"></a><a name="math_toolkit.dist.dist_ref.nmp.lower_critical_value_"></a><h5>
-<a name="id982898"></a>
+<a name="id1094515"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.lower_critical_value_">Lower
 Critical Value.</a>
 </h5>
@@ -654,7 +654,7 @@
 the <a class="link" href="nmp.html#math.dist.quantile">Quantile</a>.
 
<a name="upper_critical"></a><a name="math_toolkit.dist.dist_ref.nmp.upper_critical_value_"></a><h5>
-<a name="id982923"></a>
+<a name="id1094540"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.upper_critical_value_">Upper
 Critical Value.</a>
 </h5>
@@ -665,7 +665,7 @@
 complement of the probability</a>.
 
<a name="survival"></a><a name="math_toolkit.dist.dist_ref.nmp.survival_function"></a><h5>
-<a name="id982950"></a>
+<a name="id1094566"></a>
 <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.survival_function">Survival
 Function</a>
 </h5>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,10 +24,10 @@
</div>
<div class="section" lang="en">
<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>
+<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="id1049958"></a>
+<a name="id1158964"></a>
 <a class="link" href="future.html#math_toolkit.dist.future.adding_additional_location_and_scale_parameters">Adding
 Additional Location and Scale Parameters</a>
 </h5>
@@ -55,7 +55,7 @@
 functions.
 
<a name="math_toolkit.dist.future.an__quot_any_distribution_quot__class"></a><h5>
-<a name="id1050122"></a>
+<a name="id1159129"></a>
 <a class="link" href="future.html#math_toolkit.dist.future.an__quot_any_distribution_quot__class">An
 "any_distribution" class</a>
 </h5>
@@ -91,7 +91,7 @@
 investigation.
 
<a name="math_toolkit.dist.future.higher_level_hypothesis_tests"></a><h5>
-<a name="id1050343"></a>
+<a name="id1159350"></a>
 <a class="link" href="future.html#math_toolkit.dist.future.higher_level_hypothesis_tests">Higher
 Level Hypothesis Tests</a>
 </h5>
@@ -111,7 +111,7 @@
 expected_mean.
 
<a name="math_toolkit.dist.future.integration_with_statistical_accumulators"></a><h5>
-<a name="id1050505"></a>
+<a name="id1159512"></a>
 <a class="link" href="future.html#math_toolkit.dist.future.integration_with_statistical_accumulators">Integration
 With Statistical Accumulators</a>
 </h5>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,110 +24,112 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h3 class="title">
-<a name="math_toolkit.dist.stat_tut"></a><a class="link" href="stat_tut.html" title="Statistical Distributions Tutorial">Statistical Distributions
+<a name="math_toolkit.dist.stat_tut"></a><a class="link" href="stat_tut.html" title="Statistical Distributions Tutorial"> Statistical Distributions
 Tutorial</a>
</h3></div></div></div>
<div class="toc"><dl>
-<dt>Overview of Distributions</dt>
+<dt> Overview of Distributions</dt>
<dd><dl>
-<dt><a href="stat_tut/overview/headers.html">Headers
+<dt><a href="stat_tut/overview/headers.html"> Headers
 and Namespaces</a></dt>
-<dt><a href="stat_tut/overview/objects.html">Distributions
+<dt><a href="stat_tut/overview/objects.html"> Distributions
 are Objects</a></dt>
-<dt><a href="stat_tut/overview/generic.html">Generic
+<dt><a href="stat_tut/overview/generic.html"> Generic
 operations common to all distributions are non-member functions</a></dt>
-<dt><a href="stat_tut/overview/complements.html">Complements
- are supported too - and when to use them</a></dt>
-<dt><a href="stat_tut/overview/parameters.html">Parameters
- can be calculated</a></dt>
-<dt>Summary</dt>
-</dl></dd>
-<dt>Worked Examples</dt>
-<dd><dl>
-<dt><a href="stat_tut/weg/dist_construct_eg.html">Distribution
- Construction Example</a></dt>
-<dt><a href="stat_tut/weg/st_eg.html">Student's t
- Distribution Examples</a></dt>
-<dd><dl>
-<dt><a href="stat_tut/weg/st_eg/tut_mean_intervals.html">Calculating
- confidence intervals on the mean with the Students-t distribution</a></dt>
-<dt><a href="stat_tut/weg/st_eg/tut_mean_test.html">Testing
- a sample mean for difference from a "true" mean</a></dt>
-<dt><a href="stat_tut/weg/st_eg/tut_mean_size.html">Estimating
- how large a sample size would have to become in order to give a significant
- Students-t test result with a single sample test</a></dt>
-<dt><a href="stat_tut/weg/st_eg/two_sample_students_t.html">Comparing
- the means of two samples with the Students-t test</a></dt>
-<dt><a href="stat_tut/weg/st_eg/paired_st.html">Comparing
- two paired samples with the Student's t distribution</a></dt>
+<dt><a href="stat_tut/overview/complements.html">
+ Complements are supported too - and when to use them</a></dt>
+<dt><a href="stat_tut/overview/parameters.html">
+ Parameters can be calculated</a></dt>
+<dt> Summary</dt>
+</dl></dd>
+<dt> Worked Examples</dt>
+<dd><dl>
+<dt><a href="stat_tut/weg/dist_construct_eg.html">
+ Distribution Construction Example</a></dt>
+<dt><a href="stat_tut/weg/st_eg.html"> Student's
+ t Distribution Examples</a></dt>
+<dd><dl>
+<dt><a href="stat_tut/weg/st_eg/tut_mean_intervals.html">
+ Calculating confidence intervals on the mean with the Students-t distribution</a></dt>
+<dt><a href="stat_tut/weg/st_eg/tut_mean_test.html">
+ Testing a sample mean for difference from a "true" mean</a></dt>
+<dt><a href="stat_tut/weg/st_eg/tut_mean_size.html">
+ Estimating how large a sample size would have to become in order to give
+ a significant Students-t test result with a single sample test</a></dt>
+<dt><a href="stat_tut/weg/st_eg/two_sample_students_t.html">
+ Comparing the means of two samples with the Students-t test</a></dt>
+<dt><a href="stat_tut/weg/st_eg/paired_st.html">
+ Comparing two paired samples with the Student's t distribution</a></dt>
</dl></dd>
-<dt><a href="stat_tut/weg/cs_eg.html">Chi Squared
+<dt><a href="stat_tut/weg/cs_eg.html"> Chi Squared
 Distribution Examples</a></dt>
<dd><dl>
-<dt><a href="stat_tut/weg/cs_eg/chi_sq_intervals.html">Confidence
- Intervals on the Standard Deviation</a></dt>
-<dt><a href="stat_tut/weg/cs_eg/chi_sq_test.html">Chi-Square
- Test for the Standard Deviation</a></dt>
-<dt><a href="stat_tut/weg/cs_eg/chi_sq_size.html">Estimating
- the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</a></dt>
+<dt><a href="stat_tut/weg/cs_eg/chi_sq_intervals.html">
+ Confidence Intervals on the Standard Deviation</a></dt>
+<dt><a href="stat_tut/weg/cs_eg/chi_sq_test.html">
+ Chi-Square Test for the Standard Deviation</a></dt>
+<dt><a href="stat_tut/weg/cs_eg/chi_sq_size.html">
+ Estimating the Required Sample Sizes for a Chi-Square Test for the Standard
+ Deviation</a></dt>
</dl></dd>
-<dt><a href="stat_tut/weg/f_eg.html">F Distribution
+<dt><a href="stat_tut/weg/f_eg.html"> F Distribution
 Examples</a></dt>
-<dt><a href="stat_tut/weg/binom_eg.html">Binomial
+<dt><a href="stat_tut/weg/binom_eg.html"> Binomial
 Distribution Examples</a></dt>
<dd><dl>
-<dt><a href="stat_tut/weg/binom_eg/binomial_coinflip_example.html">Binomial
- Coin-Flipping Example</a></dt>
-<dt><a href="stat_tut/weg/binom_eg/binomial_quiz_example.html">Binomial
- Quiz Example</a></dt>
-<dt><a href="stat_tut/weg/binom_eg/binom_conf.html">Calculating
- Confidence Limits on the Frequency of Occurrence for a Binomial Distribution</a></dt>
-<dt><a href="stat_tut/weg/binom_eg/binom_size_eg.html">Estimating
- Sample Sizes for a Binomial Distribution.</a></dt>
+<dt><a href="stat_tut/weg/binom_eg/binomial_coinflip_example.html">
+ Binomial Coin-Flipping Example</a></dt>
+<dt><a href="stat_tut/weg/binom_eg/binomial_quiz_example.html">
+ Binomial Quiz Example</a></dt>
+<dt><a href="stat_tut/weg/binom_eg/binom_conf.html">
+ Calculating Confidence Limits on the Frequency of Occurrence for a Binomial
+ Distribution</a></dt>
+<dt><a href="stat_tut/weg/binom_eg/binom_size_eg.html">
+ Estimating Sample Sizes for a Binomial Distribution.</a></dt>
</dl></dd>
-<dt><a href="stat_tut/weg/geometric_eg.html">Geometric
+<dt><a href="stat_tut/weg/geometric_eg.html"> Geometric
 Distribution Examples</a></dt>
-<dt><a href="stat_tut/weg/neg_binom_eg.html">Negative
+<dt><a href="stat_tut/weg/neg_binom_eg.html"> Negative
 Binomial Distribution Examples</a></dt>
<dd><dl>
-<dt><a href="stat_tut/weg/neg_binom_eg/neg_binom_conf.html">Calculating
- Confidence Limits on the Frequency of Occurrence for the Negative Binomial
- Distribution</a></dt>
-<dt><a href="stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html">Estimating
- Sample Sizes for the Negative Binomial.</a></dt>
-<dt><a href="stat_tut/weg/neg_binom_eg/negative_binomial_example1.html">Negative
- Binomial Sales Quota Example.</a></dt>
-<dt><a href="stat_tut/weg/neg_binom_eg/negative_binomial_example2.html">Negative
- Binomial Table Printing Example.</a></dt>
+<dt><a href="stat_tut/weg/neg_binom_eg/neg_binom_conf.html">
+ Calculating Confidence Limits on the Frequency of Occurrence for the
+ Negative Binomial Distribution</a></dt>
+<dt><a href="stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html">
+ Estimating Sample Sizes for the Negative Binomial.</a></dt>
+<dt><a href="stat_tut/weg/neg_binom_eg/negative_binomial_example1.html">
+ Negative Binomial Sales Quota Example.</a></dt>
+<dt><a href="stat_tut/weg/neg_binom_eg/negative_binomial_example2.html">
+ Negative Binomial Table Printing Example.</a></dt>
</dl></dd>
-<dt><a href="stat_tut/weg/normal_example.html">Normal
+<dt><a href="stat_tut/weg/normal_example.html"> Normal
 Distribution Examples</a></dt>
-<dd><dl><dt><a href="stat_tut/weg/normal_example/normal_misc.html">Some
- Miscellaneous Examples of the Normal (Gaussian) Distribution</a></dt></dl></dd>
-<dt><a href="stat_tut/weg/nccs_eg.html">Non Central
+<dd><dl><dt><a href="stat_tut/weg/normal_example/normal_misc.html">
+ Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></dt></dl></dd>
+<dt><a href="stat_tut/weg/nccs_eg.html"> Non Central
 Chi Squared Example</a></dt>
-<dd><dl><dt><a href="stat_tut/weg/nccs_eg/nccs_power_eg.html">Tables
- of the power function of the χ2 test.</a></dt></dl></dd>
-<dt><a href="stat_tut/weg/error_eg.html">Error Handling
+<dd><dl><dt><a href="stat_tut/weg/nccs_eg/nccs_power_eg.html">
+ Tables of the power function of the χ2 test.</a></dt></dl></dd>
+<dt><a href="stat_tut/weg/error_eg.html"> Error Handling
 Example</a></dt>
-<dt><a href="stat_tut/weg/find_eg.html">Find Location
+<dt><a href="stat_tut/weg/find_eg.html"> Find Location
 and Scale Examples</a></dt>
<dd><dl>
-<dt><a href="stat_tut/weg/find_eg/find_location_eg.html">Find
- Location (Mean) Example</a></dt>
-<dt><a href="stat_tut/weg/find_eg/find_scale_eg.html">Find
- Scale (Standard Deviation) Example</a></dt>
-<dt><a href="stat_tut/weg/find_eg/find_mean_and_sd_eg.html">Find
- mean and standard deviation example</a></dt>
+<dt><a href="stat_tut/weg/find_eg/find_location_eg.html">
+ Find Location (Mean) Example</a></dt>
+<dt><a href="stat_tut/weg/find_eg/find_scale_eg.html">
+ Find Scale (Standard Deviation) Example</a></dt>
+<dt><a href="stat_tut/weg/find_eg/find_mean_and_sd_eg.html">
+ Find mean and standard deviation example</a></dt>
</dl></dd>
-<dt><a href="stat_tut/weg/nag_library.html">Comparison
+<dt><a href="stat_tut/weg/nag_library.html"> Comparison
 with C, R, FORTRAN-style Free Functions</a></dt>
-<dt><a href="stat_tut/weg/c_sharp.html">Using the
+<dt><a href="stat_tut/weg/c_sharp.html"> Using the
 Distributions from Within C#</a></dt>
</dl></dd>
-<dt><a href="stat_tut/variates.html">Random Variates
+<dt><a href="stat_tut/variates.html"> Random Variates
 and Distribution Parameters</a></dt>
-<dt><a href="stat_tut/dist_params.html">Discrete Probability
+<dt><a href="stat_tut/dist_params.html"> Discrete Probability
 Distributions</a></dt>
</dl></div>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h4 class="title">
-<a name="math_toolkit.dist.stat_tut.dist_params"></a><a class="link" href="dist_params.html" title="Discrete Probability Distributions">Discrete Probability
+<a name="math_toolkit.dist.stat_tut.dist_params"></a><a class="link" href="dist_params.html" title="Discrete Probability Distributions"> Discrete Probability
Distributions</a>
</h4></div></div></div>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,22 +24,23 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h4 class="title">
-<a name="math_toolkit.dist.stat_tut.overview"></a><a class="link" href="overview.html" title="Overview of Distributions">Overview of Distributions</a>
+<a name="math_toolkit.dist.stat_tut.overview"></a><a class="link" href="overview.html" title="Overview of Distributions"> Overview of Distributions</a>
</h4></div></div></div>
<div class="toc"><dl>
-<dt><a href="overview/headers.html">Headers
+<dt><a href="overview/headers.html"> Headers
 and Namespaces</a></dt>
-<dt><a href="overview/objects.html">Distributions
+<dt><a href="overview/objects.html"> Distributions
 are Objects</a></dt>
-<dt><a href="overview/generic.html">Generic
+<dt><a href="overview/generic.html"> Generic
 operations common to all distributions are non-member functions</a></dt>
-<dt><a href="overview/complements.html">Complements
- are supported too - and when to use them</a></dt>
-<dt><a href="overview/parameters.html">Parameters
- can be calculated</a></dt>
-<dt>Summary</dt>
+<dt><a href="overview/complements.html">
+ Complements are supported too - and when to use them</a></dt>
+<dt><a href="overview/parameters.html">
+ Parameters can be calculated</a></dt>
+<dt> Summary</dt>
</dl></div>
-<a name="complements"></a>
+<a name="complements"></a>
+ 
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.stat_tut.overview.complements"></a><a class="link" href="complements.html" title="Complements are supported too - and when to use them">Complements
- are supported too - and when to use them</a>
+<a name="math_toolkit.dist.stat_tut.overview.complements"></a><a class="link" href="complements.html" title="Complements are supported too - and when to use them">
+ Complements are supported too - and when to use them</a>
</h5></div></div></div>

 Often you don't want the value of the CDF, but its complement, which
@@ -70,6 +70,8 @@
</tr>
<tr><td align="left" valign="top">

+ 
+
 Critical values are just quantiles
 

@@ -103,13 +105,17 @@
 
</td></tr>
</table></div>
-<a name="why_complements"></a><div class="tip"><table border="0" summary="Tip">
+<a name="why_complements"></a>
+ 
+<div class="tip"><table border="0" summary="Tip">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../../../../../doc/src/images/tip.png"></td>
<th align="left">Tip</th>
</tr>
<tr><td align="left" valign="top">

+ 
+
 Why bother with complements anyway?
 

@@ -180,6 +186,8 @@
 This assumes that the 0.00001 value is either a constant, or can be
 computed by some manner other than subtracting 0.99999 from 1.
 
+
+ 
</td></tr>
</table></div>
</div>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/generic.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/generic.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/generic.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.stat_tut.overview.generic"></a><a class="link" href="generic.html" title="Generic operations common to all distributions are non-member functions">Generic
+<a name="math_toolkit.dist.stat_tut.overview.generic"></a><a class="link" href="generic.html" title="Generic operations common to all distributions are non-member functions"> Generic
 operations common to all distributions are non-member functions</a>
</h5></div></div></div>

@@ -59,6 +59,8 @@
</tr>
<tr><td align="left" valign="top">

+ 
+
 Random numbers that approximate Quantiles of
 Distributions
 
@@ -100,6 +102,8 @@
</tr>
<tr><td align="left" valign="top">

+ 
+
 Random Variates and Distribution Parameters
 

@@ -190,6 +194,8 @@
</tr>
<tr><td align="left" valign="top">

+ 
+
 Discrete Probability Distributions

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/headers.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/headers.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/headers.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.stat_tut.overview.headers"></a><a class="link" href="headers.html" title="Headers and Namespaces">Headers
+<a name="math_toolkit.dist.stat_tut.overview.headers"></a><a class="link" href="headers.html" title="Headers and Namespaces"> Headers
and Namespaces</a>
</h5></div></div></div>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/objects.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/objects.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/objects.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.stat_tut.overview.objects"></a><a class="link" href="objects.html" title="Distributions are Objects">Distributions
+<a name="math_toolkit.dist.stat_tut.overview.objects"></a><a class="link" href="objects.html" title="Distributions are Objects"> Distributions
are Objects</a>
</h5></div></div></div>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/parameters.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/parameters.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/parameters.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.stat_tut.overview.parameters"></a><a class="link" href="parameters.html" title="Parameters can be calculated">Parameters
- can be calculated</a>
+<a name="math_toolkit.dist.stat_tut.overview.parameters"></a><a class="link" href="parameters.html" title="Parameters can be calculated">
+ Parameters can be calculated</a>
</h5></div></div></div>

Sometimes it's the parameters that define the distribution that you need

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/summary.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/summary.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/summary.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.stat_tut.overview.summary"></a><a class="link" href="summary.html" title="Summary">Summary</a>
+<a name="math_toolkit.dist.stat_tut.overview.summary"></a><a class="link" href="summary.html" title="Summary"> Summary</a>
</h5></div></div></div>
<div class="itemizedlist"><ul type="disc">
<li>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/variates.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/variates.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/variates.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h4 class="title">
-<a name="math_toolkit.dist.stat_tut.variates"></a><a class="link" href="variates.html" title="Random Variates and Distribution Parameters">Random Variates
+<a name="math_toolkit.dist.stat_tut.variates"></a><a class="link" href="variates.html" title="Random Variates and Distribution Parameters"> Random Variates
and Distribution Parameters</a>
</h4></div></div></div>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,90 +24,96 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h4 class="title">
-<a name="math_toolkit.dist.stat_tut.weg"></a><a class="link" href="weg.html" title="Worked Examples">Worked Examples</a>
+<a name="math_toolkit.dist.stat_tut.weg"></a><a class="link" href="weg.html" title="Worked Examples"> Worked Examples</a>
</h4></div></div></div>
<div class="toc"><dl>
-<dt><a href="weg/dist_construct_eg.html">Distribution
- Construction Example</a></dt>
-<dt><a href="weg/st_eg.html">Student's t
- Distribution Examples</a></dt>
+<dt><a href="weg/dist_construct_eg.html">
+ Distribution Construction Example</a></dt>
+<dt><a href="weg/st_eg.html"> Student's
+ t Distribution Examples</a></dt>
<dd><dl>
-<dt><a href="weg/st_eg/tut_mean_intervals.html">Calculating
- confidence intervals on the mean with the Students-t distribution</a></dt>
-<dt><a href="weg/st_eg/tut_mean_test.html">Testing
- a sample mean for difference from a "true" mean</a></dt>
-<dt><a href="weg/st_eg/tut_mean_size.html">Estimating
- how large a sample size would have to become in order to give a significant
- Students-t test result with a single sample test</a></dt>
-<dt><a href="weg/st_eg/two_sample_students_t.html">Comparing
- the means of two samples with the Students-t test</a></dt>
-<dt><a href="weg/st_eg/paired_st.html">Comparing
- two paired samples with the Student's t distribution</a></dt>
+<dt><a href="weg/st_eg/tut_mean_intervals.html">
+ Calculating confidence intervals on the mean with the Students-t distribution</a></dt>
+<dt><a href="weg/st_eg/tut_mean_test.html">
+ Testing a sample mean for difference from a "true" mean</a></dt>
+<dt><a href="weg/st_eg/tut_mean_size.html">
+ Estimating how large a sample size would have to become in order to give
+ a significant Students-t test result with a single sample test</a></dt>
+<dt><a href="weg/st_eg/two_sample_students_t.html">
+ Comparing the means of two samples with the Students-t test</a></dt>
+<dt><a href="weg/st_eg/paired_st.html">
+ Comparing two paired samples with the Student's t distribution</a></dt>
</dl></dd>
-<dt><a href="weg/cs_eg.html">Chi Squared
+<dt><a href="weg/cs_eg.html"> Chi Squared
 Distribution Examples</a></dt>
<dd><dl>
-<dt><a href="weg/cs_eg/chi_sq_intervals.html">Confidence
- Intervals on the Standard Deviation</a></dt>
-<dt><a href="weg/cs_eg/chi_sq_test.html">Chi-Square
- Test for the Standard Deviation</a></dt>
-<dt><a href="weg/cs_eg/chi_sq_size.html">Estimating
- the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</a></dt>
+<dt><a href="weg/cs_eg/chi_sq_intervals.html">
+ Confidence Intervals on the Standard Deviation</a></dt>
+<dt><a href="weg/cs_eg/chi_sq_test.html">
+ Chi-Square Test for the Standard Deviation</a></dt>
+<dt><a href="weg/cs_eg/chi_sq_size.html">
+ Estimating the Required Sample Sizes for a Chi-Square Test for the Standard
+ Deviation</a></dt>
</dl></dd>
-<dt><a href="weg/f_eg.html">F Distribution
+<dt><a href="weg/f_eg.html"> F Distribution
 Examples</a></dt>
-<dt><a href="weg/binom_eg.html">Binomial
+<dt><a href="weg/binom_eg.html"> Binomial
 Distribution Examples</a></dt>
<dd><dl>
-<dt><a href="weg/binom_eg/binomial_coinflip_example.html">Binomial
- Coin-Flipping Example</a></dt>
-<dt><a href="weg/binom_eg/binomial_quiz_example.html">Binomial
- Quiz Example</a></dt>
-<dt><a href="weg/binom_eg/binom_conf.html">Calculating
- Confidence Limits on the Frequency of Occurrence for a Binomial Distribution</a></dt>
-<dt><a href="weg/binom_eg/binom_size_eg.html">Estimating
- Sample Sizes for a Binomial Distribution.</a></dt>
+<dt><a href="weg/binom_eg/binomial_coinflip_example.html">
+ Binomial Coin-Flipping Example</a></dt>
+<dt><a href="weg/binom_eg/binomial_quiz_example.html">
+ Binomial Quiz Example</a></dt>
+<dt><a href="weg/binom_eg/binom_conf.html">
+ Calculating Confidence Limits on the Frequency of Occurrence for a Binomial
+ Distribution</a></dt>
+<dt><a href="weg/binom_eg/binom_size_eg.html">
+ Estimating Sample Sizes for a Binomial Distribution.</a></dt>
</dl></dd>
-<dt><a href="weg/geometric_eg.html">Geometric
+<dt><a href="weg/geometric_eg.html"> Geometric
 Distribution Examples</a></dt>
-<dt><a href="weg/neg_binom_eg.html">Negative
+<dt><a href="weg/neg_binom_eg.html"> Negative
 Binomial Distribution Examples</a></dt>
<dd><dl>
-<dt><a href="weg/neg_binom_eg/neg_binom_conf.html">Calculating
- Confidence Limits on the Frequency of Occurrence for the Negative Binomial
- Distribution</a></dt>
-<dt><a href="weg/neg_binom_eg/neg_binom_size_eg.html">Estimating
- Sample Sizes for the Negative Binomial.</a></dt>
-<dt><a href="weg/neg_binom_eg/negative_binomial_example1.html">Negative
- Binomial Sales Quota Example.</a></dt>
-<dt><a href="weg/neg_binom_eg/negative_binomial_example2.html">Negative
- Binomial Table Printing Example.</a></dt>
+<dt><a href="weg/neg_binom_eg/neg_binom_conf.html">
+ Calculating Confidence Limits on the Frequency of Occurrence for the
+ Negative Binomial Distribution</a></dt>
+<dt><a href="weg/neg_binom_eg/neg_binom_size_eg.html">
+ Estimating Sample Sizes for the Negative Binomial.</a></dt>
+<dt><a href="weg/neg_binom_eg/negative_binomial_example1.html">
+ Negative Binomial Sales Quota Example.</a></dt>
+<dt><a href="weg/neg_binom_eg/negative_binomial_example2.html">
+ Negative Binomial Table Printing Example.</a></dt>
</dl></dd>
-<dt><a href="weg/normal_example.html">Normal
+<dt><a href="weg/normal_example.html"> Normal
 Distribution Examples</a></dt>
-<dd><dl><dt><a href="weg/normal_example/normal_misc.html">Some
- Miscellaneous Examples of the Normal (Gaussian) Distribution</a></dt></dl></dd>
-<dt><a href="weg/nccs_eg.html">Non Central
+<dd><dl><dt><a href="weg/normal_example/normal_misc.html">
+ Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></dt></dl></dd>
+<dt><a href="weg/nccs_eg.html"> Non Central
 Chi Squared Example</a></dt>
-<dd><dl><dt><a href="weg/nccs_eg/nccs_power_eg.html">Tables
- of the power function of the χ2 test.</a></dt></dl></dd>
-<dt><a href="weg/error_eg.html">Error Handling
+<dd><dl><dt><a href="weg/nccs_eg/nccs_power_eg.html">
+ Tables of the power function of the χ2 test.</a></dt></dl></dd>
+<dt><a href="weg/error_eg.html"> Error Handling
 Example</a></dt>
-<dt><a href="weg/find_eg.html">Find Location
+<dt><a href="weg/find_eg.html"> Find Location
 and Scale Examples</a></dt>
<dd><dl>
-<dt><a href="weg/find_eg/find_location_eg.html">Find
- Location (Mean) Example</a></dt>
-<dt><a href="weg/find_eg/find_scale_eg.html">Find
- Scale (Standard Deviation) Example</a></dt>
-<dt><a href="weg/find_eg/find_mean_and_sd_eg.html">Find
- mean and standard deviation example</a></dt>
+<dt><a href="weg/find_eg/find_location_eg.html">
+ Find Location (Mean) Example</a></dt>
+<dt><a href="weg/find_eg/find_scale_eg.html">
+ Find Scale (Standard Deviation) Example</a></dt>
+<dt><a href="weg/find_eg/find_mean_and_sd_eg.html">
+ Find mean and standard deviation example</a></dt>
</dl></dd>
-<dt><a href="weg/nag_library.html">Comparison
+<dt><a href="weg/nag_library.html"> Comparison
 with C, R, FORTRAN-style Free Functions</a></dt>
-<dt><a href="weg/c_sharp.html">Using the
+<dt><a href="weg/c_sharp.html"> Using the
 Distributions from Within C#</a></dt>
</dl></div>
+
+ 
+
+ 
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,18 +24,19 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.binom_eg"></a><a class="link" href="binom_eg.html" title="Binomial Distribution Examples">Binomial
+<a name="math_toolkit.dist.stat_tut.weg.binom_eg"></a><a class="link" href="binom_eg.html" title="Binomial Distribution Examples"> Binomial
Distribution Examples</a>
</h5></div></div></div>
<div class="toc"><dl>
-<dt><a href="binom_eg/binomial_coinflip_example.html">Binomial
- Coin-Flipping Example</a></dt>
-<dt><a href="binom_eg/binomial_quiz_example.html">Binomial
- Quiz Example</a></dt>
-<dt><a href="binom_eg/binom_conf.html">Calculating
- Confidence Limits on the Frequency of Occurrence for a Binomial Distribution</a></dt>
-<dt><a href="binom_eg/binom_size_eg.html">Estimating
- Sample Sizes for a Binomial Distribution.</a></dt>
+<dt><a href="binom_eg/binomial_coinflip_example.html">
+ Binomial Coin-Flipping Example</a></dt>
+<dt><a href="binom_eg/binomial_quiz_example.html">
+ Binomial Quiz Example</a></dt>
+<dt><a href="binom_eg/binom_conf.html">
+ Calculating Confidence Limits on the Frequency of Occurrence for a Binomial
+ Distribution</a></dt>
+<dt><a href="binom_eg/binom_size_eg.html">
+ Estimating Sample Sizes for a Binomial Distribution.</a></dt>
</dl></div>

See also the reference documentation for the <a class="link" href="../../dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,9 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h6 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.binom_eg.binom_conf"></a><a class="link" href="binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution">Calculating
- Confidence Limits on the Frequency of Occurrence for a Binomial Distribution</a>
+<a name="math_toolkit.dist.stat_tut.weg.binom_eg.binom_conf"></a><a class="link" href="binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution">
+ Calculating Confidence Limits on the Frequency of Occurrence for a Binomial
+ Distribution</a>
</h6></div></div></div>

Imagine you have a process that follows a binomial distribution: for

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h6 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.binom_eg.binom_size_eg"></a><a class="link" href="binom_size_eg.html" title="Estimating Sample Sizes for a Binomial Distribution.">Estimating
- Sample Sizes for a Binomial Distribution.</a>
+<a name="math_toolkit.dist.stat_tut.weg.binom_eg.binom_size_eg"></a><a class="link" href="binom_size_eg.html" title="Estimating Sample Sizes for a Binomial Distribution.">
+ Estimating Sample Sizes for a Binomial Distribution.</a>
</h6></div></div></div>

Imagine you have a critical component that you know will fail in 1

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,36 +24,48 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h6 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.binom_eg.binomial_coinflip_example"></a><a class="link" href="binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">Binomial
- Coin-Flipping Example</a>
+<a name="math_toolkit.dist.stat_tut.weg.binom_eg.binomial_coinflip_example"></a><a class="link" href="binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">
+ Binomial Coin-Flipping Example</a>
</h6></div></div></div>

- An example of a <a href="http://en.wikipedia.org/wiki/Bernoulli_process" target="_top">Bernoulli
- process</a> is coin flipping. A variable in such a sequence may
- be called a Bernoulli variable.
- 
+ 

- This example shows using the Binomial distribution to predict the probability
- of heads and tails when throwing a coin.
- 
+ An example of a <a href="http://en.wikipedia.org/wiki/Bernoulli_process" target="_top">Bernoulli
+ process</a> is coin flipping. A variable in such a sequence may
+ be called a Bernoulli variable.
+ 

- The number of correct answers (say heads), X, is distributed as a binomial
- random variable with binomial distribution parameters number of trials
- (flips) n = 10 and probability (success_fraction) of getting a head
- p = 0.5 (a 'fair' coin).
- 
+ 

- (Our coin is assumed fair, but we could easily change the success_fraction
- parameter p from 0.5 to some other value to simulate an unfair coin,
- say 0.6 for one with chewing gum on the tail, so it is more likely
- to fall tails down and heads up).
- 
+ This example shows using the Binomial distribution to predict the
+ probability of heads and tails when throwing a coin.
+ 

- First we need some includes and using statements to be able to use
- the binomial distribution, some std input and output, and get started:
- 
+ 

-
+ The number of correct answers (say heads), X, is distributed as a
+ binomial random variable with binomial distribution parameters number
+ of trials (flips) n = 10 and probability (success_fraction) of getting
+ a head p = 0.5 (a 'fair' coin).
+ 
+
+ 
+
+ (Our coin is assumed fair, but we could easily change the success_fraction
+ parameter p from 0.5 to some other value to simulate an unfair coin,
+ say 0.6 for one with chewing gum on the tail, so it is more likely
+ to fall tails down and heads up).
+ 
+
+ 
+
+ First we need some includes and using statements to be able to use
+ the binomial distribution, some std input and output, and get started:
+ 
+
+ 
+
+

<pre class="programlisting">#include <boost/math/distributions/binomial.hpp>
 using boost::math::binomial;
@@ -69,17 +81,23 @@
 try
 {</pre>

- 
+ 

- See note <a class="link" href="binomial_coinflip_example.html#coinflip_eg_catch">with the catch block</a>
- about why a try and catch block is always a good idea.
- 
+ 

- First, construct a binomial distribution with parameters success_fraction
- 1/2, and how many flips.
- 
+ See note <a class="link" href="binomial_coinflip_example.html#coinflip_eg_catch">with the catch block</a>
+ about why a try and catch block is always a good idea.
+ 

-
+ 
+
+ First, construct a binomial distribution with parameters success_fraction
+ 1/2, and how many flips.
+ 
+
+ 
+
+

<pre class="programlisting">const double success_fraction = 0.5; // = 50% = 1/2 for a 'fair' coin.
int flips = 10;
@@ -87,12 +105,16 @@

cout.precision(4);</pre>

- 
+ 

- Then some examples of using Binomial moments (and echoing the parameters).
- 
+ 

-
+ Then some examples of using Binomial moments (and echoing the parameters).
+ 
+
+ 
+
+

<pre class="programlisting">cout << "From " << flips << " one can expect to get on average "
 << mean(flip) << " heads (or tails)." << endl;
@@ -108,104 +130,141 @@
cout << "Skewness if success_fraction is " << flip.success_fraction()
 << " is " << skewness(flip) << endl << endl; // Expect zero for a 'fair' coin.</pre>

- 
+ 

- Now we show a variety of predictions on the probability of heads:
- 
+ 

-
+ Now we show a variety of predictions on the probability of heads:
+ 
+
+ 
+
+

<pre class="programlisting">cout << "For " << flip.trials() << " coin flips: " << endl;
cout << "Probability of getting no heads is " << pdf(flip, 0) << endl;
cout << "Probability of getting at least one head is " << 1. - pdf(flip, 0) << endl;</pre>

- 
+ 

- When we want to calculate the probability for a range or values we
- can sum the PDF's:
- 
+ 

-
+ When we want to calculate the probability for a range or values we
+ can sum the PDF's:
+ 
+
+ 
+
+

<pre class="programlisting">cout << "Probability of getting 0 or 1 heads is "
 << pdf(flip, 0) + pdf(flip, 1) << endl; // sum of exactly == probabilities</pre>

- 
+ 

- Or we can use the cdf.
- 
+ 

-
+ Or we can use the cdf.
+ 
+
+ 
+
+

<pre class="programlisting">cout << "Probability of getting 0 or 1 (<= 1) heads is " << cdf(flip, 1) << endl;
cout << "Probability of getting 9 or 10 heads is " << pdf(flip, 9) + pdf(flip, 10) << endl;</pre>

- 
+ 

- Note that using
- 
+ 

-
+ Note that using
+ 
+
+ 
+
+

<pre class="programlisting">cout << "Probability of getting 9 or 10 heads is " << 1. - cdf(flip, 8) << endl;</pre>

- 
+ 

- is less accurate than using the complement
- 
+ 

-
+ is less accurate than using the complement
+ 
+
+ 
+
+

<pre class="programlisting">cout << "Probability of getting 9 or 10 heads is " << cdf(complement(flip, 8)) << endl;</pre>

- 
+ 

- Since the subtraction may involve <a href="http://docs.sun.com/source/806-3568/ncg_goldberg.html" target="_top">cancellation
- error</a>, where as <code class="computeroutput">cdf(complement(flip, 8))</code>
- does not use such a subtraction internally, and so does not exhibit
- the problem.
- 
+ 

- To get the probability for a range of heads, we can either add the
- pdfs for each number of heads
- 
+ Since the subtraction may involve <a href="http://docs.sun.com/source/806-3568/ncg_goldberg.html" target="_top">cancellation
+ error</a>, where as <code class="computeroutput">cdf(complement(flip, 8))</code> does not use such a subtraction
+ internally, and so does not exhibit the problem.
+ 

-
+ 
+
+ To get the probability for a range of heads, we can either add the
+ pdfs for each number of heads
+ 
+
+ 
+
+

<pre class="programlisting">cout << "Probability of between 4 and 6 heads (4 or 5 or 6) is "
 // P(X == 4) + P(X == 5) + P(X == 6)
 << pdf(flip, 4) + pdf(flip, 5) + pdf(flip, 6) << endl;</pre>

- 
+ 

- But this is probably less efficient than using the cdf
- 
+ 

-
+ But this is probably less efficient than using the cdf
+ 
+
+ 
+
+

<pre class="programlisting">cout << "Probability of between 4 and 6 heads (4 or 5 or 6) is "
 // P(X <= 6) - P(X <= 3) == P(X < 4)
 << cdf(flip, 6) - cdf(flip, 3) << endl;</pre>

- 
+ 

- Certainly for a bigger range like, 3 to 7
- 
+ 

-
+ Certainly for a bigger range like, 3 to 7
+ 
+
+ 
+
+

<pre class="programlisting">cout << "Probability of between 3 and 7 heads (3, 4, 5, 6 or 7) is "
 // P(X <= 7) - P(X <= 2) == P(X < 3)
 << cdf(flip, 7) - cdf(flip, 2) << endl;
cout << endl;</pre>

- 
+ 

- Finally, print two tables of probability for the exactly
- and at least a number of heads.
- 
+ 

-
+ Finally, print two tables of probability for the exactly
+ and at least a number of heads.
+ 
+
+ 
+
+

<pre class="programlisting">// Print a table of probability for the exactly a number of heads.
cout << "Probability of getting exactly (==) heads" << endl;
@@ -229,42 +288,58 @@
 << probability * 100. << "%"<< endl;
} // for i</pre>

- 
+ 

- The last (0 to 10 heads) must, of course, be 100% probability.
- 
+ 

-
+ The last (0 to 10 heads) must, of course, be 100% probability.
+ 
+
+ 
+
+

<pre class="programlisting">}
catch(const std::exception& e)
{
 //</pre>

- 
-<a name="coinflip_eg_catch"></a>
- It is always essential to include try & catch blocks because default
- policies are to throw exceptions on arguments that are out of domain
- or cause errors like numeric-overflow.
- 
+ 

- Lacking try & catch blocks, the program will abort, whereas the
- message below from the thrown exception will give some helpful clues
- as to the cause of the problem.
- 
+ <a name="coinflip_eg_catch"></a>
+ 

-
+ It is always essential to include try & catch blocks because
+ default policies are to throw exceptions on arguments that are out
+ of domain or cause errors like numeric-overflow.
+ 
+
+ 
+
+ Lacking try & catch blocks, the program will abort, whereas the
+ message below from the thrown exception will give some helpful clues
+ as to the cause of the problem.
+ 
+
+ 
+
+

<pre class="programlisting"> std::cout <<
 "\n""Message from thrown exception was:\n " << e.what() << std::endl;
}
</pre>

+ 
+
 

 See binomial_coinflip_example.cpp
 for full source code, the program output looks like this:
 
+
+
+
<pre class="programlisting">Using Binomial distribution to predict how many heads and tails.
From 10 one can expect to get on average 5 heads (or tails).
Mode is 5
@@ -311,6 +386,8 @@
9 0.999 or 1 in 1.001, or 99.9%
10 1 or 1 in 1, or 100%
</pre>
+
+ 
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,27 +24,33 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h6 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example"></a><a class="link" href="binomial_quiz_example.html" title="Binomial Quiz Example">Binomial
- Quiz Example</a>
+<a name="math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example"></a><a class="link" href="binomial_quiz_example.html" title="Binomial Quiz Example">
+ Binomial Quiz Example</a>
</h6></div></div></div>

- A multiple choice test has four possible answers to each of 16 questions.
- A student guesses the answer to each question, so the probability of
- getting a correct answer on any given question is one in four, a quarter,
- 1/4, 25% or fraction 0.25. The conditions of the binomial experiment
- are assumed to be met: n = 16 questions constitute the trials; each
- question results in one of two possible outcomes (correct or incorrect);
- the probability of being correct is 0.25 and is constant if no knowledge
- about the subject is assumed; the questions are answered independently
- if the student's answer to a question in no way influences his/her
- answer to another question.
- 
+ 

- First, we need to be able to use the binomial distribution constructor
- (and some std input/output, of course).
- 
+ A multiple choice test has four possible answers to each of 16 questions.
+ A student guesses the answer to each question, so the probability
+ of getting a correct answer on any given question is one in four,
+ a quarter, 1/4, 25% or fraction 0.25. The conditions of the binomial
+ experiment are assumed to be met: n = 16 questions constitute the
+ trials; each question results in one of two possible outcomes (correct
+ or incorrect); the probability of being correct is 0.25 and is constant
+ if no knowledge about the subject is assumed; the questions are answered
+ independently if the student's answer to a question in no way influences
+ his/her answer to another question.
+ 
+
+ 
+
+ First, we need to be able to use the binomial distribution constructor
+ (and some std input/output, of course).
+ 

-
+ 
+
+

<pre class="programlisting">#include <boost/math/distributions/binomial.hpp>
 using boost::math::binomial;
@@ -60,38 +66,50 @@

</pre>

- 
+ 

- The number of correct answers, X, is distributed as a binomial random
- variable with binomial distribution parameters: questions n and success
- fraction probability p. So we construct a binomial distribution:
- 
+ 

-
+ The number of correct answers, X, is distributed as a binomial random
+ variable with binomial distribution parameters: questions n and success
+ fraction probability p. So we construct a binomial distribution:
+ 
+
+ 
+
+

<pre class="programlisting">int questions = 16; // All the questions in the quiz.
int answers = 4; // Possible answers to each question.
double success_fraction = 1. / answers; // If a random guess, p = 1/4 = 0.25.
binomial quiz(questions, success_fraction);</pre>

- 
+ 

- and display the distribution parameters we used thus:
- 
+ 

-
+ and display the distribution parameters we used thus:
+ 
+
+ 
+
+

<pre class="programlisting">cout << "In a quiz with " << quiz.trials()
 << " questions and with a probability of guessing right of "
 << quiz.success_fraction() * 100 << " %"
 << " or 1 in " << static_cast<int>(1. / quiz.success_fraction()) << endl;</pre>

- 
+ 

- Show a few probabilities of just guessing:
- 
+ 

-
+ Show a few probabilities of just guessing:
+ 
+
+ 
+
+

<pre class="programlisting">cout << "Probability of getting none right is " << pdf(quiz, 0) << endl; // 0.010023
cout << "Probability of getting exactly one right is " << pdf(quiz, 1) << endl;
@@ -102,7 +120,10 @@
cout << "Probability of getting all " << questions << " answers right by chance is "
 << pdf(quiz, questions) << endl;</pre>

- 
+ 
+
+
+
<pre class="programlisting">Probability of getting none right is 0.0100226
Probability of getting exactly one right is 0.0534538
Probability of getting exactly two right is 0.133635
@@ -110,13 +131,20 @@
Probability of getting exactly all 16 answers right by chance is 2.32831e-010
</pre>

- These don't give any encouragement to guessers!
- 
+ 

- We can tabulate the 'getting exactly right' ( == ) probabilities thus:
- 
+ These don't give any encouragement to guessers!
+ 

-
+ 
+
+ We can tabulate the 'getting exactly right' ( == ) probabilities
+ thus:
+ 
+
+ 
+
+

<pre class="programlisting">cout << "\n" "Guessed Probability" << right << endl;
for (int successes = 0; successes <= questions; successes++)
@@ -126,7 +154,10 @@
}
cout << endl;</pre>

- 
+ 
+
+
+
<pre class="programlisting">Guessed Probability
 0 0.0100226
 1 0.0534538
@@ -147,101 +178,152 @@
16 2.32831e-010
</pre>

- Then we can add the probabilities of some 'exactly right' like this:
- 
+ 

-
+ Then we can add the probabilities of some 'exactly right' like this:
+ 
+
+ 
+
+

<pre class="programlisting">cout << "Probability of getting none or one right is " << pdf(quiz, 0) + pdf(quiz, 1) << endl;</pre>

- 
+ 
+
+
+
<pre class="programlisting">Probability of getting none or one right is 0.0634764
</pre>

- But if more than a couple of scores are involved, it is more convenient
- (and may be more accurate) to use the Cumulative Distribution Function
- (cdf) instead:
- 
+ 

-
+ But if more than a couple of scores are involved, it is more convenient
+ (and may be more accurate) to use the Cumulative Distribution Function
+ (cdf) instead:
+ 
+
+ 
+
+

<pre class="programlisting">cout << "Probability of getting none or one right is " << cdf(quiz, 1) << endl;</pre>

- 
+ 
+
+
+
<pre class="programlisting">Probability of getting none or one right is 0.0634764
</pre>

- Since the cdf is inclusive, we can get the probability of getting up
- to 10 right ( <= )
- 
+ 

-
+ Since the cdf is inclusive, we can get the probability of getting
+ up to 10 right ( <= )
+ 
+
+ 
+
+

<pre class="programlisting">cout << "Probability of getting <= 10 right (to fail) is " << cdf(quiz, 10) << endl;</pre>

- 
+ 
+
+
+
<pre class="programlisting">Probability of getting <= 10 right (to fail) is 0.999715
</pre>

- To get the probability of getting 11 or more right (to pass), it is
- tempting to use
+ 
+
+ To get the probability of getting 11 or more right (to pass), it
+ is tempting to use

<pre class="programlisting">1 - cdf(quiz, 10)</pre>

- to get the probability of > 10
- 
+ to get the probability of > 10
+ 

-
+ 
+
+

<pre class="programlisting">cout << "Probability of getting > 10 right (to pass) is " << 1 - cdf(quiz, 10) << endl;</pre>

- 
+ 
+
+
+
<pre class="programlisting">Probability of getting > 10 right (to pass) is 0.000285239
</pre>

- But this should be resisted in favor of using the complement function.
- <a class="link" href="../../overview/complements.html#why_complements">Why complements?</a>
- 
+ 

-
+ But this should be resisted in favor of using the complement function.
+ <a class="link" href="../../overview/complements.html#why_complements">Why complements?</a>
+ 
+
+ 
+
+

<pre class="programlisting">cout << "Probability of getting > 10 right (to pass) is " << cdf(complement(quiz, 10)) << endl;</pre>

- 
+ 
+
+
+
<pre class="programlisting">Probability of getting > 10 right (to pass) is 0.000285239
</pre>

- And we can check that these two, <= 10 and > 10, add up to unity.
- 
+ 

-
+ And we can check that these two, <= 10 and > 10, add up to
+ unity.
+ 
+
+ 
+
+

<pre class="programlisting">BOOST_ASSERT((cdf(quiz, 10) + cdf(complement(quiz, 10))) == 1.);</pre>

- 
+ 

- If we want a < rather than a <= test, because the CDF is inclusive,
- we must subtract one from the score.
- 
+ 

-
+ If we want a < rather than a <= test, because the CDF is inclusive,
+ we must subtract one from the score.
+ 
+
+ 
+
+

<pre class="programlisting">cout << "Probability of getting less than " << pass_score
 << " (< " << pass_score << ") answers right by guessing is "
 << cdf(quiz, pass_score -1) << endl;</pre>

- 
+ 
+
+
+
<pre class="programlisting">Probability of getting less than 11 (< 11) answers right by guessing is 0.999715
</pre>

- and similarly to get a >= rather than a > test we also need to
- subtract one from the score (and can again check the sum is unity).
- This is because if the cdf is inclusive, then
- its complement must be exclusive otherwise there
- would be one possible outcome counted twice!
- 
+ 

-
+ and similarly to get a >= rather than a > test we also need
+ to subtract one from the score (and can again check the sum is unity).
+ This is because if the cdf is inclusive, then
+ its complement must be exclusive otherwise there
+ would be one possible outcome counted twice!
+ 
+
+ 
+
+

<pre class="programlisting">cout << "Probability of getting at least " << pass_score
 << "(>= " << pass_score << ") answers right by guessing is "
@@ -250,14 +332,21 @@

BOOST_ASSERT((cdf(quiz, pass_score -1) + cdf(complement(quiz, pass_score-1))) == 1);</pre>

- 
+ 
+
+
+
<pre class="programlisting">Probability of getting at least 11 (>= 11) answers right by guessing is 0.000285239, only 1 in 3505.83
</pre>

- Finally we can tabulate some probabilities:
- 
+ 

-
+ Finally we can tabulate some probabilities:
+ 
+
+ 
+
+

<pre class="programlisting">cout << "\n" "At most (<=)""\n""Guessed OK Probability" << right << endl;
for (int score = 0; score <= questions; score++)
@@ -267,7 +356,10 @@
}
cout << endl;</pre>

- 
+ 
+
+
+
<pre class="programlisting">At most (<=)
Guessed OK Probability
 0 0.01002259576
@@ -289,7 +381,9 @@
16 1
</pre>

-
+ 
+
+

<pre class="programlisting">cout << "\n" "At least (>)""\n""Guessed OK Probability" << right << endl;
for (int score = 0; score <= questions; score++)
@@ -298,7 +392,10 @@
 << cdf(complement(quiz, score)) << endl;
}</pre>

- 
+ 
+
+
+
<pre class="programlisting">At least (>)
Guessed OK Probability
 0 0.9899774042
@@ -320,15 +417,21 @@
16 0
</pre>

- We now consider the probabilities of ranges
- of correct guesses.
- 
+ 

- First, calculate the probability of getting a range of guesses right,
- by adding the exact probabilities of each from low ... high.
- 
+ We now consider the probabilities of ranges
+ of correct guesses.
+ 

-
+ 
+
+ First, calculate the probability of getting a range of guesses right,
+ by adding the exact probabilities of each from low ... high.
+ 
+
+ 
+
+

<pre class="programlisting">int low = 3; // Getting at least 3 right.
int high = 5; // Getting as most 5 right.
@@ -342,26 +445,40 @@
 << low << " and " << high << " answers right by guessing is "
 << sum << endl; // 0.61323</pre>

- 
+ 
+
+
+
<pre class="programlisting">Probability of getting between 3 and 5 answers right by guessing is 0.6132
</pre>

- Or, usually better, we can use the difference of cdfs instead:
- 
+ 

-
+ Or, usually better, we can use the difference of cdfs instead:
+ 
+
+ 
+
+

<pre class="programlisting">cout << "Probability of getting between " << low << " and " << high << " answers right by guessing is "
 << cdf(quiz, high) - cdf(quiz, low - 1) << endl; // 0.61323</pre>

- 
+ 
+
+
+
<pre class="programlisting">Probability of getting between 3 and 5 answers right by guessing is 0.6132
</pre>

- And we can also try a few more combinations of high and low choices:
- 
+ 

-
+ And we can also try a few more combinations of high and low choices:
+ 
+
+ 
+
+

<pre class="programlisting">low = 1; high = 6;
cout << "Probability of getting between " << low << " and " << high << " answers right by guessing is "
@@ -373,22 +490,32 @@
cout << "Probability of getting between " << low << " and " << high << " answers right by guessing is "
 << cdf(quiz, high) - cdf(quiz, low - 1) << endl; // 4 <= x 4 P = 0.22520</pre>

- 
+ 
+
+
+
<pre class="programlisting">Probability of getting between 1 and 6 answers right by guessing is 0.9104
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="id924547"></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
- Binomial distribution moments</a>
- </h5>

- Using moments of the distribution, we can say more about the spread
- of results from guessing.
- 
+ <a name="math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.using_binomial_distribution_moments"></a>
+ 
+<h5>
+<a name="id1033847"></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
+ Binomial distribution moments</a>
+ </h5>
+
+ 
+
+ Using moments of the distribution, we can say more about the spread
+ of results from guessing.
+ 

-
+ 
+
+

<pre class="programlisting">cout << "By guessing, on average, one can expect to get " << mean(quiz) << " correct answers." << endl;
cout << "Standard deviation is " << standard_deviation(quiz) << endl;
@@ -398,23 +525,33 @@
cout << "Mode (the most frequent) is " << mode(quiz) << endl;
cout << "Skewness is " << skewness(quiz) << endl;</pre>

- 
+ 
+
+
+
<pre class="programlisting">By guessing, on average, one can expect to get 4 correct answers.
Standard deviation is 1.732
So about 2/3 will lie within 1 standard deviation and get between 3 and 5 correct.
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="id924919"></a>
- <a class="link" href="binomial_quiz_example.html#math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.quantiles">Quantiles</a>
- </h5>

- The quantiles (percentiles or percentage points) for a few probability
- levels:
- 
+ <a name="math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.quantiles"></a>
+ 
+<h5>
+<a name="id1034282"></a>
+ <a class="link" href="binomial_quiz_example.html#math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.quantiles">Quantiles</a>
+ </h5>
+
+ 
+
+ The quantiles (percentiles or percentage points) for a few probability
+ levels:
+ 

-
+ 
+
+

<pre class="programlisting">cout << "Quartiles " << quantile(quiz, 0.25) << " to "
 << quantile(complement(quiz, 0.25)) << endl; // Quartiles
@@ -432,11 +569,16 @@
cout << "If guessing then percentiles 1 to 99% will get " << quantile(quiz, 0.01)
 << " to " << quantile(complement(quiz, 0.01)) << " right." << endl;</pre>

- 
+ 

- Notice that these output integral values because the default policy
- is <code class="computeroutput">integer_round_outwards</code>.
- 
+ 
+
+ Notice that these output integral values because the default policy
+ is <code class="computeroutput">integer_round_outwards</code>.
+ 
+
+
+
<pre class="programlisting">Quartiles 2 to 5
1 standard deviation 2 to 5
Deciles 1 to 6
@@ -445,74 +587,111 @@
2 to 98% 0 to 8
</pre>

- Quantiles values are controlled by the <a class="link" href="../../../../policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">discrete
- quantile policy</a> chosen. The default is <code class="computeroutput">integer_round_outwards</code>,
- so the lower quantile is rounded down, and the upper quantile is rounded
- up.
- 
+ 

- But we might believe that the real values tell us a little more - see
- <a class="link" href="../../../../policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
- Discrete Quantile Policy</a>.
- 
+ Quantiles values are controlled by the <a class="link" href="../../../../policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">discrete
+ quantile policy</a> chosen. The default is <code class="computeroutput">integer_round_outwards</code>,
+ so the lower quantile is rounded down, and the upper quantile is
+ rounded up.
+ 
+
+ 
+
+ But we might believe that the real values tell us a little more -
+ see <a class="link" href="../../../../policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
+ Discrete Quantile Policy</a>.
+ 
+
+ 
+
+ We could control the policy for all
+ distributions by
+ 

- We could control the policy for all
- distributions by
- 
+
+
<pre class="programlisting">#define BOOST_MATH_DISCRETE_QUANTILE_POLICY real

at the head of the program would make this policy apply
</pre>

- to this one, and only, translation
- unit.
- 
+ 

- Or we can now create a (typedef for) policy that has discrete quantiles
- real (here avoiding any 'using namespaces ...' statements):
- 
+ #define BOOST_MATH_DISCRETE_QUANTILE_POLICY real
+ 



+<pre class="programlisting">at the head of the program would make this policy apply
+</pre>
+
+ 
+
+ at the head of the program would make this policy apply to this
+ one, and only, translation unit.
+ 
+
+ 
+
+ Or we can now create a (typedef for) policy that has discrete quantiles
+ real (here avoiding any 'using namespaces ...' statements):
+ 
+
+ 
+
+
+
<pre class="programlisting">using boost::math::policies::policy;
using boost::math::policies::discrete_quantile;
using boost::math::policies::real;
using boost::math::policies::integer_round_outwards; // Default.
typedef boost::math::policies::policy<discrete_quantile<real> > real_quantile_policy;</pre>

- 
+ 

- Add a custom binomial distribution called
+ 
+
+ Add a custom binomial distribution called

<pre class="programlisting">real_quantile_binomial</pre>

- that uses
+ that uses

<pre class="programlisting">real_quantile_policy</pre>

- 
+ 

-
+ 
+
+

<pre class="programlisting">using boost::math::binomial_distribution;
typedef binomial_distribution<double, real_quantile_policy> real_quantile_binomial;</pre>

- 
+ 

- Construct an object of this custom distribution:
- 
+ 

-
+ Construct an object of this custom distribution:
+ 
+
+ 
+
+

<pre class="programlisting">real_quantile_binomial quiz_real(questions, success_fraction);</pre>

- 
+ 

- And use this to show some quantiles - that now have real rather than
- integer values.
- 
+ 

-
+ And use this to show some quantiles - that now have real rather than
+ integer values.
+ 
+
+ 
+
+

<pre class="programlisting">cout << "Quartiles " << quantile(quiz, 0.25) << " to "
 << quantile(complement(quiz_real, 0.25)) << endl; // Quartiles 2 to 4.6212
@@ -530,7 +709,10 @@
cout << "If guessing, then percentiles 1 to 99% will get " << quantile(quiz_real, 0.01)
 << " to " << quantile(complement(quiz_real, 0.01)) << " right." << endl;</pre>

- 
+ 
+
+
+
<pre class="programlisting">Real Quantiles
Quartiles 2 to 4.621
1 standard deviation 2.665 to 4.194
@@ -541,6 +723,8 @@
If guessing then percentiles 1 to 99% will get 0 to 7.788 right.
</pre>

+ 
+
 See binomial_quiz_example.cpp
 for full source code and output.

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/c_sharp.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/c_sharp.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/c_sharp.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.c_sharp"></a><a class="link" href="c_sharp.html" title="Using the Distributions from Within C#">Using the
+<a name="math_toolkit.dist.stat_tut.weg.c_sharp"></a><a class="link" href="c_sharp.html" title="Using the Distributions from Within C#"> Using the
Distributions from Within C#</a>
</h5></div></div></div>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,16 +24,17 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.cs_eg"></a><a class="link" href="cs_eg.html" title="Chi Squared Distribution Examples">Chi Squared
+<a name="math_toolkit.dist.stat_tut.weg.cs_eg"></a><a class="link" href="cs_eg.html" title="Chi Squared Distribution Examples"> Chi Squared
Distribution Examples</a>
</h5></div></div></div>
<div class="toc"><dl>
-<dt><a href="cs_eg/chi_sq_intervals.html">Confidence
- Intervals on the Standard Deviation</a></dt>
-<dt><a href="cs_eg/chi_sq_test.html">Chi-Square
- Test for the Standard Deviation</a></dt>
-<dt><a href="cs_eg/chi_sq_size.html">Estimating
- the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</a></dt>
+<dt><a href="cs_eg/chi_sq_intervals.html">
+ Confidence Intervals on the Standard Deviation</a></dt>
+<dt><a href="cs_eg/chi_sq_test.html">
+ Chi-Square Test for the Standard Deviation</a></dt>
+<dt><a href="cs_eg/chi_sq_size.html">
+ Estimating the Required Sample Sizes for a Chi-Square Test for the Standard
+ Deviation</a></dt>
</dl></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h6 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.cs_eg.chi_sq_intervals"></a><a class="link" href="chi_sq_intervals.html" title="Confidence Intervals on the Standard Deviation">Confidence
- Intervals on the Standard Deviation</a>
+<a name="math_toolkit.dist.stat_tut.weg.cs_eg.chi_sq_intervals"></a><a class="link" href="chi_sq_intervals.html" title="Confidence Intervals on the Standard Deviation">
+ Confidence Intervals on the Standard Deviation</a>
</h6></div></div></div>

 Once you have calculated the standard deviation for your data, a legitimate
@@ -139,7 +139,7 @@
 is between 0.00551 and 0.00729.
 
<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="id908116"></a>
+<a name="id1018612"></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
 intervals as a function of the number of observations</a>
 </h5>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,9 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h6 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.cs_eg.chi_sq_size"></a><a class="link" href="chi_sq_size.html" title="Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation">Estimating
- the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</a>
+<a name="math_toolkit.dist.stat_tut.weg.cs_eg.chi_sq_size"></a><a class="link" href="chi_sq_size.html" title="Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation">
+ Estimating the Required Sample Sizes for a Chi-Square Test for the Standard
+ Deviation</a>
</h6></div></div></div>

Suppose we conduct a Chi Squared test for standard deviation and the

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h6 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.cs_eg.chi_sq_test"></a><a class="link" href="chi_sq_test.html" title="Chi-Square Test for the Standard Deviation">Chi-Square
- Test for the Standard Deviation</a>
+<a name="math_toolkit.dist.stat_tut.weg.cs_eg.chi_sq_test"></a><a class="link" href="chi_sq_test.html" title="Chi-Square Test for the Standard Deviation">
+ Chi-Square Test for the Standard Deviation</a>
</h6></div></div></div>

We use this test to determine whether the standard deviation of a sample

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,28 +24,34 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.dist_construct_eg"></a><a class="link" href="dist_construct_eg.html" title="Distribution Construction Example">Distribution
- Construction Example</a>
+<a name="math_toolkit.dist.stat_tut.weg.dist_construct_eg"></a><a class="link" href="dist_construct_eg.html" title="Distribution Construction Example">
+ Distribution Construction Example</a>
</h5></div></div></div>

 See distribution_construction.cpp
 for full source code.
 

- The structure of distributions is rather different from some other statistical
- libraries, for example in less object-oriented language like FORTRAN
- and C, that provide a few arguments to each free function. This library
- provides each distribution as a template C++ class. A distribution is
- constructed with a few arguments, and then member and non-member functions
- are used to find values of the distribution, often a function of a random
- variate.
- 
+ 

- First we need some includes to access the negative binomial distribution
- (and the binomial, beta and gamma too).
- 
+ The structure of distributions is rather different from some other
+ statistical libraries, for example in less object-oriented language
+ like FORTRAN and C, that provide a few arguments to each free function.
+ This library provides each distribution as a template C++ class. A
+ distribution is constructed with a few arguments, and then member and
+ non-member functions are used to find values of the distribution, often
+ a function of a random variate.
+ 
+
+ 
+
+ First we need some includes to access the negative binomial distribution
+ (and the binomial, beta and gamma too).
+ 

-
+ 
+
+

<pre class="programlisting">#include <boost/math/distributions/negative_binomial.hpp> // for negative_binomial_distribution
 using boost::math::negative_binomial_distribution; // default type is double.
@@ -55,167 +61,240 @@
#include <boost/math/distributions/gamma.hpp> // for gamma_distribution.
#include <boost/math/distributions/normal.hpp> // for normal_distribution.</pre>

- 
+ 

- Several examples of constructing distributions follow:
- 
+ 

- First, a negative binomial distribution with 8 successes and a success
- fraction 0.25, 25% or 1 in 4, is constructed like this:
- 
+ Several examples of constructing distributions follow:
+ 

-
+ 
+
+ First, a negative binomial distribution with 8 successes and a success
+ fraction 0.25, 25% or 1 in 4, is constructed like this:
+ 
+
+ 
+
+

<pre class="programlisting">boost::math::negative_binomial_distribution<double> mydist0(8., 0.25);</pre>

- 
+ 

- But this is inconveniently long, so we might be tempted to write
- 
+ 

-
+ But this is inconveniently long, so we might be tempted to write
+ 
+
+ 
+
+

<pre class="programlisting">using namespace boost::math;</pre>

- 
+ 

- but this might risk ambiguity with names in std random so *much better
- is explicit <code class="computeroutput">using boost::math:: </code> * ... statements like
- 
+ 

-
+ but this might risk ambiguity with names in std random so *much better
+ is explicit <code class="computeroutput">using boost::math:: </code> * ... statements like
+ 
+
+ 
+
+

<pre class="programlisting">using boost::math::negative_binomial_distribution;</pre>

- 
+ 

- and we can still reduce typing.
- 
+ 

- Since the vast majority of applications use will be using double precision,
- the template argument to the distribution (RealType) defaults to type
- double, so we can also write:
- 
+ and we can still reduce typing.
+ 

-
+ 
+
+ Since the vast majority of applications use will be using double precision,
+ the template argument to the distribution (RealType) defaults to type
+ double, so we can also write:
+ 
+
+ 
+
+

<pre class="programlisting">negative_binomial_distribution<> mydist9(8., 0.25); // Uses default RealType = double.</pre>

- 
+ 

- But the name "negative_binomial_distribution" is still inconveniently
- long, so for most distributions, a convenience typedef is provided, for
- example:
- 
+ 
+
+ But the name "negative_binomial_distribution" is still inconveniently
+ long, so for most distributions, a convenience typedef is provided,
+ for example:
+ 
+
+
+
<pre class="programlisting">typedef negative_binomial_distribution<double> negative_binomial; // Reserved name of type double.
</pre>
+
+ 
<div class="caution"><table border="0" summary="Caution">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../../../doc/src/images/caution.png"></td>
<th align="left">Caution</th>
</tr>
<tr><td align="left" valign="top">
- This convenience typedef is not provided if a
- clash would occur with the name of a function: currently only "beta"
- and "gamma" fall into this category.
- </td></tr>
+ This convenience typedef is not provided if
+ a clash would occur with the name of a function: currently only "beta"
+ and "gamma" fall into this category.
+ </td></tr>
</table></div>

- So, after a using statement,
- 
+ 

-
+ So, after a using statement,
+ 
+
+ 
+
+

<pre class="programlisting">using boost::math::negative_binomial;</pre>

- 
+ 

- we have a convenient typedef to <code class="computeroutput">negative_binomial_distribution<double></code>:
- 
+ 

-
+ we have a convenient typedef to <code class="computeroutput">negative_binomial_distribution<double></code>:
+ 
+
+ 
+
+

<pre class="programlisting">negative_binomial mydist(8., 0.25);</pre>

- 
+ 

- Some more examples using the convenience typedef:
- 
+ 

-
+ Some more examples using the convenience typedef:
+ 
+
+ 
+
+

<pre class="programlisting">negative_binomial mydist10(5., 0.4); // Both arguments double.</pre>

- 
+ 

- And automatic conversion takes place, so you can use integers and floats:
- 
+ 

-
+ And automatic conversion takes place, so you can use integers and floats:
+ 
+
+ 
+
+

<pre class="programlisting">negative_binomial mydist11(5, 0.4); // Using provided typedef double, int and double arguments.</pre>

- 
+ 

- This is probably the most common usage.
- 
+ 

-
+ This is probably the most common usage.
+ 
+
+ 
+
+

<pre class="programlisting">negative_binomial mydist12(5., 0.4F); // Double and float arguments.
negative_binomial mydist13(5, 1); // Both arguments integer.</pre>

- 
+ 

- Similarly for most other distributions like the binomial.
- 
+ 

-
+ Similarly for most other distributions like the binomial.
+ 
+
+ 
+
+

<pre class="programlisting">binomial mybinomial(1, 0.5); // is more concise than
binomial_distribution<> mybinomd1(1, 0.5);</pre>

- 
+ 

- For cases when the typdef distribution name would clash with a math special
- function (currently only beta and gamma) the typedef is deliberately
- not provided, and the longer version of the name must be used. For example
- do not use:
- 
+ 
+
+ For cases when the typdef distribution name would clash with a math
+ special function (currently only beta and gamma) the typedef is deliberately
+ not provided, and the longer version of the name must be used. For
+ example do not use:
+ 
+
+
+
<pre class="programlisting">using boost::math::beta;
beta mybetad0(1, 0.5); // Error beta is a math FUNCTION!
</pre>

- Which produces the error messages:
- 
+ 
+
+ Which produces the error messages:
+ 
+
+
+
<pre class="programlisting">error C2146: syntax error : missing ';' before identifier 'mybetad0'
warning C4551: function call missing argument list
error C3861: 'mybetad0': identifier not found
</pre>

- Instead you should use:
- 
+ 

-
+ Instead you should use:
+ 
+
+ 
+
+

<pre class="programlisting">using boost::math::beta_distribution;
beta_distribution<> mybetad1(1, 0.5);</pre>

- 
+ 

- or for the gamma distribution:
- 
+ 

-
+ or for the gamma distribution:
+ 
+
+ 
+
+

<pre class="programlisting">gamma_distribution<> mygammad1(1, 0.5);</pre>

- 
+ 

- We can, of course, still provide the type explicitly thus:
- 
+ 

-
+ We can, of course, still provide the type explicitly thus:
+ 
+
+ 
+
+

<pre class="programlisting">// Explicit double precision:
negative_binomial_distribution<double> mydist1(8., 0.25);
@@ -238,40 +317,65 @@
// Explicit long double precision:
negative_binomial_distribution<long double> mydist7(8., 0.25);</pre>

- 
+ 

- And if you have your own RealType called MyFPType, for example NTL RR
- (an arbitrary precision type), then we can write:
- 
+ 
+
+ And if you have your own RealType called MyFPType, for example NTL
+ RR (an arbitrary precision type), then we can write:
+ 
+
+
+
<pre class="programlisting">negative_binomial_distribution<MyFPType> mydist6(8, 1); // Integer arguments -> MyFPType.
</pre>
-<a name="math_toolkit.dist.stat_tut.weg.dist_construct_eg.default_arguments_to_distribution_constructors_"></a><h6>
-<a name="id898706"></a>
- <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>
-
- Note that default constructor arguments are only provided for some distributions.
- So if you wrongly assume a default argument you will get an error message,
- for example:
- 
+
+ <a name="math_toolkit.dist.stat_tut.weg.dist_construct_eg.default_arguments_to_distribution_constructors_"></a>
+ 
+<h6>
+<a name="id1007733"></a>
+ <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>
+
+ 
+
+ Note that default constructor arguments are only provided for some
+ distributions. So if you wrongly assume a default argument you will
+ get an error message, for example:
+ 
+
+
+
<pre class="programlisting">negative_binomial_distribution<> mydist8;
</pre>
+
+
+
<pre class="programlisting">error C2512 no appropriate default constructor available.</pre>

- No default constructors are provided for the negative binomial, because
- it is difficult to chose any sensible default values for this distribution.
- For other distributions, like the normal distribution, it is obviously
- very useful to provide 'standard' defaults for the mean and standard
- deviation thus:
- 
+ 
+
+ No default constructors are provided for the negative binomial, because
+ it is difficult to chose any sensible default values for this distribution.
+ For other distributions, like the normal distribution, it is obviously
+ very useful to provide 'standard' defaults for the mean and standard
+ deviation thus:
+ 
+
+
+
<pre class="programlisting">normal_distribution(RealType mean = 0, RealType sd = 1);
</pre>

- So in this case we can write:
- 
+ 

-
+ So in this case we can write:
+ 
+
+ 
+
+

<pre class="programlisting"> using boost::math::normal;

@@ -282,9 +386,13 @@
 return 0;
} // int main()</pre>

- 
+ 
+
+ 
+
+ There is no useful output from this program, of course.
+ 

- There is no useful output from this program, of course.
 
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.error_eg"></a><a class="link" href="error_eg.html" title="Error Handling Example">Error Handling
+<a name="math_toolkit.dist.stat_tut.weg.error_eg"></a><a class="link" href="error_eg.html" title="Error Handling Example"> Error Handling
 Example</a>
</h5></div></div></div>

@@ -43,44 +43,69 @@
 the policy.
 

- The following example demonstrates the effect of setting the macro BOOST_MATH_DOMAIN_ERROR_POLICY
- when an invalid argument is encountered. For the purposes of this example,
- we'll pass a negative degrees of freedom parameter to the student's t
- distribution.
- 
+ 

- Since we know that this is a single file program we could just add:
- 
+ The following example demonstrates the effect of setting the macro
+ BOOST_MATH_DOMAIN_ERROR_POLICY when an invalid argument is encountered.
+ For the purposes of this example, we'll pass a negative degrees of
+ freedom parameter to the student's t distribution.
+ 
+
+ 
+
+ Since we know that this is a single file program we could just add:
+ 
+
+
+
<pre class="programlisting">#define BOOST_MATH_DOMAIN_ERROR_POLICY ignore_error
</pre>

- to the top of the source file to change the default policy to one that
- simply returns a NaN when a domain error occurs. Alternatively we could
- use:
- 
+ 
+
+ to the top of the source file to change the default policy to one that
+ simply returns a NaN when a domain error occurs. Alternatively we could
+ use:
+ 
+
+
+
<pre class="programlisting">#define BOOST_MATH_DOMAIN_ERROR_POLICY errno_on_error
</pre>

- To ensure the <code class="computeroutput">::errno</code>
- is set when a domain error occurs as well as returning a NaN.
- 
+ 

- This is safe provided the program consists of a single translation unit
- and we place the define before
- any #includes. Note that should we add the define after the includes
- then it will have no effect! A warning such as:
- 
-<pre class="programlisting">warning C4005: 'BOOST_MATH_OVERFLOW_ERROR_POLICY' : macro redefinition</pre>
+ To ensure the <code class="computeroutput">::errno</code>
+ is set when a domain error occurs as well as returning a NaN.
+ 

- is a certain sign that it will not have the desired
- effect.
- 
+ 

- We'll begin our sample program with the needed includes:
- 
+ This is safe provided the program consists of a single translation
+ unit and we place the define before
+ any #includes. Note that should we add the define after the includes
+ then it will have no effect! A warning such as:
+ 



+<pre class="programlisting">warning C4005: 'BOOST_MATH_OVERFLOW_ERROR_POLICY' : macro redefinition</pre>
+
+ 
+
+ is a certain sign that it will not have the desired
+ effect.
+ 
+
+ 
+
+ We'll begin our sample program with the needed includes:
+ 
+
+ 
+
+
+
<pre class="programlisting">// Boost
#include <boost/math/distributions/students_t.hpp>
 using boost::math::students_t; // Probability of students_t(df, t).
@@ -96,14 +121,18 @@
#include <cstddef>
 // using ::errno</pre>

- 
+ 

- Next we'll define the program's main() to call the student's t distribution
- with an invalid degrees of freedom parameter, the program is set up to
- handle either an exception or a NaN:
- 
+ 

-
+ Next we'll define the program's main() to call the student's t distribution
+ with an invalid degrees of freedom parameter, the program is set up
+ to handle either an exception or a NaN:
+ 
+
+ 
+
+

<pre class="programlisting">int main()
{
@@ -139,11 +168,16 @@
 return 0;
} // int main()</pre>

- 
+ 

- Here's what the program output looks like with a default build (one that
- does throw exceptions):
- 
+ 
+
+ Here's what the program output looks like with a default build (one
+ that does throw exceptions):
+ 
+
+
+
<pre class="programlisting">Example error handling using Student's t function.
BOOST_MATH_DOMAIN_ERROR_POLICY is set to: throw_on_error

@@ -152,30 +186,52 @@
 Degrees of freedom argument is -1, but must be > 0 !
</pre>

- Alternatively let's build with:
- 
+ 
+
+ Alternatively let's build with:
+ 
+
+
+
<pre class="programlisting">#define BOOST_MATH_DOMAIN_ERROR_POLICY ignore_error
</pre>

- Now the program output is:
- 
+ 
+
+ Now the program output is:
+ 
+
+
+
<pre class="programlisting">Example error handling using Student's t function.
BOOST_MATH_DOMAIN_ERROR_POLICY is set to: ignore_error
cdf returned a NaN!
</pre>

- And finally let's build with:
- 
+ 
+
+ And finally let's build with:
+ 
+
+
+
<pre class="programlisting">#define BOOST_MATH_DOMAIN_ERROR_POLICY errno_on_error
</pre>

- Which gives the output show errno:
- 
+ 
+
+ Which gives the output show errno:
+ 
+
+
+
<pre class="programlisting">Example error handling using Student's t function.
BOOST_MATH_DOMAIN_ERROR_POLICY is set to: errno_on_error
cdf returned a NaN!
errno is set to: 33
</pre>
+
+ 
<div class="caution"><table border="0" summary="Caution">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../../../doc/src/images/caution.png"></td>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.f_eg"></a><a class="link" href="f_eg.html" title="F Distribution Examples">F Distribution
+<a name="math_toolkit.dist.stat_tut.weg.f_eg"></a><a class="link" href="f_eg.html" title="F Distribution Examples"> F Distribution
Examples</a>
</h5></div></div></div>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,16 +24,16 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.find_eg"></a><a class="link" href="find_eg.html" title="Find Location and Scale Examples">Find Location
+<a name="math_toolkit.dist.stat_tut.weg.find_eg"></a><a class="link" href="find_eg.html" title="Find Location and Scale Examples"> Find Location
and Scale Examples</a>
</h5></div></div></div>
<div class="toc"><dl>
-<dt><a href="find_eg/find_location_eg.html">Find
- Location (Mean) Example</a></dt>
-<dt><a href="find_eg/find_scale_eg.html">Find
- Scale (Standard Deviation) Example</a></dt>
-<dt><a href="find_eg/find_mean_and_sd_eg.html">Find
- mean and standard deviation example</a></dt>
+<dt><a href="find_eg/find_location_eg.html">
+ Find Location (Mean) Example</a></dt>
+<dt><a href="find_eg/find_scale_eg.html">
+ Find Scale (Standard Deviation) Example</a></dt>
+<dt><a href="find_eg/find_mean_and_sd_eg.html">
+ Find mean and standard deviation example</a></dt>
</dl></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,15 +24,19 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h6 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_location_eg"></a><a class="link" href="find_location_eg.html" title="Find Location (Mean) Example">Find
- Location (Mean) Example</a>
+<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_location_eg"></a><a class="link" href="find_location_eg.html" title="Find Location (Mean) Example">
+ Find Location (Mean) Example</a>
</h6></div></div></div>

- First we need some includes to access the normal distribution, the
- algorithms to find location (and some std output of course).
- 
+ 

-
+ First we need some includes to access the normal distribution, the
+ algorithms to find location (and some std output of course).
+ 
+
+ 
+
+

<pre class="programlisting">#include <boost/math/distributions/normal.hpp> // for normal_distribution
 using boost::math::normal; // typedef provides default type is double.
@@ -54,26 +58,34 @@

</pre>

- 
+ 

- For this example, we will use the standard normal distribution, with
- mean (location) zero and standard deviation (scale) unity. This is
- also the default for this implementation.
- 
+ 

-
+ For this example, we will use the standard normal distribution, with
+ mean (location) zero and standard deviation (scale) unity. This is
+ also the default for this implementation.
+ 
+
+ 
+
+

<pre class="programlisting">normal N01; // Default 'standard' normal distribution with zero mean and
double sd = 1.; // normal default standard deviation is 1.</pre>

- 
+ 

- Suppose we want to find a different normal distribution whose mean
- is shifted so that only fraction p (here 0.001 or 0.1%) are below a
- certain chosen limit (here -2, two standard deviations).
- 
+ 

-
+ Suppose we want to find a different normal distribution whose mean
+ is shifted so that only fraction p (here 0.001 or 0.1%) are below
+ a certain chosen limit (here -2, two standard deviations).
+ 
+
+ 
+
+

<pre class="programlisting">double z = -2.; // z to give prob p
double p = 0.001; // only 0.1% below z
@@ -87,44 +99,66 @@
 << ", has " << "fraction > " << z
 << ", p = " << cdf(complement(N01, z)) << endl; // Note: uses complement.</pre>

- 
+ 
+
+
+
<pre class="programlisting">Normal distribution with mean = 0, standard deviation 1, has fraction <= -2, p = 0.0227501
Normal distribution with mean = 0, standard deviation 1, has fraction > -2, p = 0.97725
</pre>

- We can now use ''find_location'' to give a new offset mean.
- 
+ 

-
+ We can now use ''find_location'' to give a new offset mean.
+ 
+
+ 
+
+

<pre class="programlisting">double l = find_location<normal>(z, p, sd);
cout << "offset location (mean) = " << l << endl;</pre>

- 
+ 

- that outputs:
- 
+ 
+
+ that outputs:
+ 
+
+
+
<pre class="programlisting">offset location (mean) = 1.09023
</pre>

- showing that we need to shift the mean just over one standard deviation
- from its previous value of zero.
- 
+ 

- Then we can check that we have achieved our objective by constructing
- a new distribution with the offset mean (but same standard deviation):
- 
+ showing that we need to shift the mean just over one standard deviation
+ from its previous value of zero.
+ 

-
+ 
+
+ Then we can check that we have achieved our objective by constructing
+ a new distribution with the offset mean (but same standard deviation):
+ 
+
+ 
+
+

<pre class="programlisting">normal np001pc(l, sd); // Same standard_deviation (scale) but with mean (location) shifted.</pre>

- 
+ 

- And re-calculating the fraction below our chosen limit.
- 
+ 

-
+ And re-calculating the fraction below our chosen limit.
+ 
+
+ 
+
+

<pre class="programlisting">cout << "Normal distribution with mean = " << l
 << " has " << "fraction <= " << z
@@ -133,37 +167,53 @@
 << " has " << "fraction > " << z
 << ", p = " << cdf(complement(np001pc, z)) << endl;</pre>

- 
+ 
+
+
+
<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="id965461"></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
- Error Handling from find_location</a>
- </h5>
-
- We can also control the policy for handling various errors. For example,
- we can define a new (possibly unwise) policy to ignore domain errors
- ('bad' arguments).
- 

- Unless we are using the boost::math namespace, we will need:
- 
+ <a name="math_toolkit.dist.stat_tut.weg.find_eg.find_location_eg.controlling_error_handling_from_find_location"></a>
+ 
+<h5>
+<a name="id1073980"></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
+ Error Handling from find_location</a>
+ </h5>

-
+ 
+
+ We can also control the policy for handling various errors. For example,
+ we can define a new (possibly unwise) policy to ignore domain errors
+ ('bad' arguments).
+ 
+
+ 
+
+ Unless we are using the boost::math namespace, we will need:
+ 
+
+ 
+
+

<pre class="programlisting">using boost::math::policies::policy;
using boost::math::policies::domain_error;
using boost::math::policies::ignore_error;</pre>

- 
+ 

- Using a typedef is often convenient, especially if it is re-used, although
- it is not required, as the various examples below show.
- 
+ 

-
+ Using a typedef is often convenient, especially if it is re-used,
+ although it is not required, as the various examples below show.
+ 
+
+ 
+
+

<pre class="programlisting">typedef policy<domain_error<ignore_error> > ignore_domain_policy;
// find_location with new policy, using typedef.
@@ -175,15 +225,19 @@
// A new policy, ignoring domain errors, without using a typedef.
l = find_location<normal>(z, p, sd, policy<domain_error<ignore_error> >());</pre>

- 
+ 

- If we want to use a probability that is the <a class="link" href="../../overview.html#complements">complement
- of our probability</a>, we should not even think of writing <code class="computeroutput">find_location<normal>(z, 1 - p, sd)</code>,
- but, <a class="link" href="../../overview/complements.html#why_complements">to avoid loss of accuracy</a>,
- use the complement version.
- 
+ 

-
+ If we want to use a probability that is the <a class="link" href="../../overview.html#complements">complement
+ of our probability</a>, we should not even think of writing <code class="computeroutput">find_location<normal>(z, 1 - p, sd)</code>,
+ but, <a class="link" href="../../overview/complements.html#why_complements">to avoid loss of accuracy</a>,
+ use the complement version.
+ 
+
+ 
+
+

<pre class="programlisting">z = 2.;
double q = 0.95; // = 1 - p; // complement.
@@ -196,11 +250,11 @@
 << "fraction > " << z << " = " << cdf(complement(np95pc, z)) << endl;
</pre>

- 
+ 

 See find_location_example.cpp
- for full source code: the program output looks like this:
- 
+ for full source code: the program output looks like this:
+
<pre class="programlisting">Example: Find location (mean).
Normal distribution with mean = 0, standard deviation 1, has fraction <= -2, p = 0.0227501
Normal distribution with mean = 0, standard deviation 1, has fraction > -2, p = 0.97725
@@ -210,6 +264,8 @@
Normal distribution with mean = 0.355146 has fraction <= 2 = 0.95
Normal distribution with mean = 0.355146 has fraction > 2 = 0.05
</pre>
+
+ 
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,15 +24,19 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h6 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg"></a><a class="link" href="find_mean_and_sd_eg.html" title="Find mean and standard deviation example">Find
- mean and standard deviation example</a>
+<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg"></a><a class="link" href="find_mean_and_sd_eg.html" title="Find mean and standard deviation example">
+ Find mean and standard deviation example</a>
</h6></div></div></div>

- First we need some includes to access the normal distribution, the
- algorithms to find location and scale (and some std output of course).
- 
+ 

-
+ First we need some includes to access the normal distribution, the
+ algorithms to find location and scale (and some std output of course).
+ 
+
+ 
+
+

<pre class="programlisting">#include <boost/math/distributions/normal.hpp> // for normal_distribution
 using boost::math::normal; // typedef provides default type is double.
@@ -55,78 +59,108 @@
 using std::exception;
</pre>

- 
-<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="id973322"></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
- find_location and find_scale to meet dispensing and measurement specifications</a>
- </h5>
-
- Consider an example from K Krishnamoorthy, Handbook of Statistical
- Distributions with Applications, ISBN 1-58488-635-8, (2006) p 126,
- example 10.3.7.
- 
+ 

- "A machine is set to pack 3 kg of ground beef per pack. Over a
- long period of time it is found that the average packed was 3 kg with
- a standard deviation of 0.1 kg. Assume the packing is normally distributed."
- 
+ <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="id1081208"></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
+ find_location and find_scale to meet dispensing and measurement specifications</a>
+ </h5>

- We start by constructing a normal distribution with the given parameters:
- 
+ 

-
+ Consider an example from K Krishnamoorthy, Handbook of Statistical
+ Distributions with Applications, ISBN 1-58488-635-8, (2006) p 126,
+ example 10.3.7.
+ 
+
+ 
+
+ "A machine is set to pack 3 kg of ground beef per pack. Over
+ a long period of time it is found that the average packed was 3 kg
+ with a standard deviation of 0.1 kg. Assume the packing is normally
+ distributed."
+ 
+
+ 
+
+ We start by constructing a normal distribution with the given parameters:
+ 
+
+ 
+
+

<pre class="programlisting">double mean = 3.; // kg
double standard_deviation = 0.1; // kg
normal packs(mean, standard_deviation);</pre>

- 
+ 

- We can then find the fraction (or %) of packages that weigh more than
- 3.1 kg.
- 
+ 

-
+ We can then find the fraction (or %) of packages that weigh more
+ than 3.1 kg.
+ 
+
+ 
+
+

<pre class="programlisting">double max_weight = 3.1; // kg
cout << "Percentage of packs > " << max_weight << " is "
<< cdf(complement(packs, max_weight)) * 100. << endl; // P(X > 3.1)</pre>

- 
+ 

- We might want to ensure that 95% of packs are over a minimum weight
- specification, then we want the value of the mean such that P(X <
- 2.9) = 0.05.
- 
+ 

- Using the mean of 3 kg, we can estimate the fraction of packs that
- fail to meet the specification of 2.9 kg.
- 
+ We might want to ensure that 95% of packs are over a minimum weight
+ specification, then we want the value of the mean such that P(X <
+ 2.9) = 0.05.
+ 

-
+ 
+
+ Using the mean of 3 kg, we can estimate the fraction of packs that
+ fail to meet the specification of 2.9 kg.
+ 
+
+ 
+
+

<pre class="programlisting">double minimum_weight = 2.9;
cout <<"Fraction of packs <= " << minimum_weight << " with a mean of " << mean
 << " is " << cdf(complement(packs, minimum_weight)) << endl;
// fraction of packs <= 2.9 with a mean of 3 is 0.841345</pre>

- 
+ 

- This is 0.84 - more than the target fraction of 0.95. If we want 95%
- to be over the minimum weight, what should we set the mean weight to
- be?
- 
+ 

- Using the KK StatCalc program supplied with the book and the method
- given on page 126 gives 3.06449.
- 
+ This is 0.84 - more than the target fraction of 0.95. If we want
+ 95% to be over the minimum weight, what should we set the mean weight
+ to be?
+ 

- We can confirm this by constructing a new distribution which we call
- 'xpacks' with a safety margin mean of 3.06449 thus:
- 
+ 

-
+ Using the KK StatCalc program supplied with the book and the method
+ given on page 126 gives 3.06449.
+ 
+
+ 
+
+ We can confirm this by constructing a new distribution which we call
+ 'xpacks' with a safety margin mean of 3.06449 thus:
+ 
+
+ 
+
+

<pre class="programlisting">double over_mean = 3.06449;
normal xpacks(over_mean, standard_deviation);
@@ -135,13 +169,17 @@
 << " is " << cdf(complement(xpacks, minimum_weight)) << endl;
// fraction of packs >= 2.9 with a mean of 3.06449 is 0.950005</pre>

- 
+ 

- Using this Math Toolkit, we can calculate the required mean directly
- thus:
- 
+ 

-
+ Using this Math Toolkit, we can calculate the required mean directly
+ thus:
+ 
+
+ 
+
+

<pre class="programlisting">double under_fraction = 0.05; // so 95% are above the minimum weight mean - sd = 2.9
double low_limit = standard_deviation;
@@ -155,69 +193,94 @@
 << " is " << cdf(complement(nominal_packs, minimum_weight)) << endl;
// Setting the packer to 3.06449 will mean that fraction of packs >= 2.9 is 0.95</pre>

- 
+ 

- This calculation is generalized as the free function called <a class="link" href="../../../dist_ref/dist_algorithms.html" title="Distribution Algorithms">find_location</a>.
- 
+ 

- To use this we will need to
- 
+ This calculation is generalized as the free function called <a class="link" href="../../../dist_ref/dist_algorithms.html" title="Distribution Algorithms">find_location</a>.
+ 

-
+ 
+
+ To use this we will need to
+ 
+
+ 
+
+

<pre class="programlisting">#include <boost/math/distributions/find_location.hpp>
 using boost::math::find_location;</pre>

- 
+ 

- and then use find_location function to find safe_mean, & construct
- a new normal distribution called 'goodpacks'.
- 
+ 

-
+ and then use find_location function to find safe_mean, & construct
+ a new normal distribution called 'goodpacks'.
+ 
+
+ 
+
+

<pre class="programlisting">double safe_mean = find_location<normal>(minimum_weight, under_fraction, standard_deviation);
normal good_packs(safe_mean, standard_deviation);</pre>

- 
+ 

- with the same confirmation as before:
- 
+ 

-
+ with the same confirmation as before:
+ 
+
+ 
+
+

<pre class="programlisting">cout << "Setting the packer to " << nominal_mean << " will mean that "
 << "fraction of packs >= " << minimum_weight
 << " is " << cdf(complement(good_packs, minimum_weight)) << endl;
// Setting the packer to 3.06449 will mean that fraction of packs >= 2.9 is 0.95</pre>

- 
-<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="id974503"></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
- Cauchy-Lorentz instead of normal distribution</a>
- </h5>
-
- After examining the weight distribution of a large number of packs,
- we might decide that, after all, the assumption of a normal distribution
- is not really justified. We might find that the fit is better to a
- <a class="link" href="../../../dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy
- Distribution</a>. This distribution has wider 'wings', so that whereas
- most of the values are closer to the mean than the normal, there are
- also more values than 'normal' that lie further from the mean than
- the normal.
- 
+ 

- This might happen because a larger than normal lump of meat is either
- included or excluded.
- 
+ <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="id1082421"></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
+ Cauchy-Lorentz instead of normal distribution</a>
+ </h5>
+
+ 
+
+ After examining the weight distribution of a large number of packs,
+ we might decide that, after all, the assumption of a normal distribution
+ is not really justified. We might find that the fit is better to
+ a <a class="link" href="../../../dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy
+ Distribution</a>. This distribution has wider 'wings', so that
+ whereas most of the values are closer to the mean than the normal,
+ there are also more values than 'normal' that lie further from the
+ mean than the normal.
+ 
+
+ 
+
+ This might happen because a larger than normal lump of meat is either
+ included or excluded.
+ 
+
+ 
+
+ We first create a <a class="link" href="../../../dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy
+ Distribution</a> with the original mean and standard deviation,
+ and estimate the fraction that lie below our minimum weight specification.
+ 

- We first create a <a class="link" href="../../../dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy
- Distribution</a> with the original mean and standard deviation,
- and estimate the fraction that lie below our minimum weight specification.
- 
+ 

-
+

<pre class="programlisting">cauchy cpacks(mean, standard_deviation);
cout << "Cauchy Setting the packer to " << mean << " will mean that "
@@ -225,29 +288,39 @@
 << " is " << cdf(complement(cpacks, minimum_weight)) << endl;
// Cauchy Setting the packer to 3 will mean that fraction of packs >= 2.9 is 0.75</pre>

- 
+ 

- Note that far fewer of the packs meet the specification, only 75% instead
- of 95%. Now we can repeat the find_location, using the cauchy distribution
- as template parameter, in place of the normal used above.
- 
+ 

-
+ Note that far fewer of the packs meet the specification, only 75%
+ instead of 95%. Now we can repeat the find_location, using the cauchy
+ distribution as template parameter, in place of the normal used above.
+ 
+
+ 
+
+

<pre class="programlisting">double lc = find_location<cauchy>(minimum_weight, under_fraction, standard_deviation);
cout << "find_location<cauchy>(minimum_weight, over fraction, standard_deviation); " << lc << endl;
// find_location<cauchy>(minimum_weight, over fraction, packs.standard_deviation()); 3.53138</pre>

- 
+ 

- Note that the safe_mean setting needs to be much higher, 3.53138 instead
- of 3.06449, so we will make rather less profit.
- 
+ 

- And again confirm that the fraction meeting specification is as expected.
- 
+ Note that the safe_mean setting needs to be much higher, 3.53138
+ instead of 3.06449, so we will make rather less profit.
+ 

-
+ 
+
+ And again confirm that the fraction meeting specification is as expected.
+ 
+
+ 
+
+

<pre class="programlisting">cauchy goodcpacks(lc, standard_deviation);
cout << "Cauchy Setting the packer to " << lc << " will mean that "
@@ -255,13 +328,17 @@
 << " is " << cdf(complement(goodcpacks, minimum_weight)) << endl;
// Cauchy Setting the packer to 3.53138 will mean that fraction of packs >= 2.9 is 0.95</pre>

- 
+ 

- Finally we could estimate the effect of a much tighter specification,
- that 99% of packs met the specification.
- 
+ 

-
+ Finally we could estimate the effect of a much tighter specification,
+ that 99% of packs met the specification.
+ 
+
+ 
+
+

<pre class="programlisting">cout << "Cauchy Setting the packer to "
 << find_location<cauchy>(minimum_weight, 0.99, standard_deviation)
@@ -269,81 +346,114 @@
 << "fraction of packs >= " << minimum_weight
 << " is " << cdf(complement(goodcpacks, minimum_weight)) << endl;</pre>

- 
+ 

- Setting the packer to 3.13263 will mean that fraction of packs >=
- 2.9 is 0.99, but will more than double the mean loss from 0.0644 to
- 0.133 kg per pack.
- 
+ 

- Of course, this calculation is not limited to packs of meat, it applies
- to dispensing anything, and it also applies to a 'virtual' material
- like any measurement.
- 
+ Setting the packer to 3.13263 will mean that fraction of packs >=
+ 2.9 is 0.99, but will more than double the mean loss from 0.0644
+ to 0.133 kg per pack.
+ 

- The only caveat is that the calculation assumes that the standard deviation
- (scale) is known with a reasonably low uncertainty, something that
- is not so easy to ensure in practice. And that the distribution is
- well defined, <a class="link" href="../../../dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal
- Distribution</a> or <a class="link" href="../../../dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy
- Distribution</a>, or some other.
- 
+ 

- If one is simply dispensing a very large number of packs, then it may
- be feasible to measure the weight of hundreds or thousands of packs.
- With a healthy 'degrees of freedom', the confidence intervals for the
- standard deviation are not too wide, typically about + and - 10% for
- hundreds of observations.
- 
+ Of course, this calculation is not limited to packs of meat, it applies
+ to dispensing anything, and it also applies to a 'virtual' material
+ like any measurement.
+ 

- For other applications, where it is more difficult or expensive to
- make many observations, the confidence intervals are depressingly wide.
- 
+ 

- See <a class="link" href="../cs_eg/chi_sq_intervals.html" title="Confidence Intervals on the Standard Deviation">Confidence
- Intervals on the standard deviation</a> for a worked example chi_square_std_dev_test.cpp
- of estimating these intervals.
- 
-<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="id975151"></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
- the scale or standard deviation</a>
- </h5>
+ The only caveat is that the calculation assumes that the standard
+ deviation (scale) is known with a reasonably low uncertainty, something
+ that is not so easy to ensure in practice. And that the distribution
+ is well defined, <a class="link" href="../../../dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal
+ Distribution</a> or <a class="link" href="../../../dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy
+ Distribution</a>, or some other.
+ 

- Alternatively, we could invest in a better (more precise) packer (or
- measuring device) with a lower standard deviation, or scale.
- 
+ 

- This might cost more, but would reduce the amount we have to 'give
- away' in order to meet the specification.
- 
+ If one is simply dispensing a very large number of packs, then it
+ may be feasible to measure the weight of hundreds or thousands of
+ packs. With a healthy 'degrees of freedom', the confidence intervals
+ for the standard deviation are not too wide, typically about + and
+ - 10% for hundreds of observations.
+ 

- To estimate how much better (how much smaller standard deviation) it
- would have to be, we need to get the 5% quantile to be located at the
- under_weight limit, 2.9
- 
+ 

-
+ For other applications, where it is more difficult or expensive to
+ make many observations, the confidence intervals are depressingly
+ wide.
+ 
+
+ 
+
+ See <a class="link" href="../cs_eg/chi_sq_intervals.html" title="Confidence Intervals on the Standard Deviation">Confidence
+ Intervals on the standard deviation</a> for a worked example
+ chi_square_std_dev_test.cpp
+ of estimating these intervals.
+ 
+
+ <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="id1083069"></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
+ the scale or standard deviation</a>
+ </h5>
+
+ 
+
+ Alternatively, we could invest in a better (more precise) packer
+ (or measuring device) with a lower standard deviation, or scale.
+ 
+
+ 
+
+ This might cost more, but would reduce the amount we have to 'give
+ away' in order to meet the specification.
+ 
+
+ 
+
+ To estimate how much better (how much smaller standard deviation)
+ it would have to be, we need to get the 5% quantile to be located
+ at the under_weight limit, 2.9
+ 
+
+ 
+
+

<pre class="programlisting">double p = 0.05; // wanted p th quantile.
cout << "Quantile of " << p << " = " << quantile(packs, p)
 << ", mean = " << packs.mean() << ", sd = " << packs.standard_deviation() << endl;</pre>

- 
+ 

- Quantile of 0.05 = 2.83551, mean = 3, sd = 0.1
- 
+ 

- With the current packer (mean = 3, sd = 0.1), the 5% quantile is at
- 2.8551 kg, a little below our target of 2.9 kg. So we know that the
- standard deviation is going to have to be smaller.
- 
+ Quantile of 0.05 = 2.83551, mean = 3, sd = 0.1
+ 

- Let's start by guessing that it (now 0.1) needs to be halved, to a
- standard deviation of 0.05 kg.
- 
+ 

-
+ With the current packer (mean = 3, sd = 0.1), the 5% quantile is
+ at 2.8551 kg, a little below our target of 2.9 kg. So we know that
+ the standard deviation is going to have to be smaller.
+ 
+
+ 
+
+ Let's start by guessing that it (now 0.1) needs to be halved, to
+ a standard deviation of 0.05 kg.
+ 
+
+ 
+
+

<pre class="programlisting">normal pack05(mean, 0.05);
cout << "Quantile of " << p << " = " << quantile(pack05, p)
@@ -355,15 +465,20 @@
 << " is " << cdf(complement(pack05, minimum_weight)) << endl;
// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.05 is 0.97725</pre>

- 
+ 

- So 0.05 was quite a good guess, but we are a little over the 2.9 target,
- so the standard deviation could be a tiny bit more. So we could do
- some more guessing to get closer, say by increasing standard deviation
- to 0.06 kg, constructing another new distribution called pack06.
- 
+ 

-
+ So 0.05 was quite a good guess, but we are a little over the 2.9
+ target, so the standard deviation could be a tiny bit more. So we
+ could do some more guessing to get closer, say by increasing standard
+ deviation to 0.06 kg, constructing another new distribution called
+ pack06.
+ 
+
+ 
+
+

<pre class="programlisting">normal pack06(mean, 0.06);
cout << "Quantile of " << p << " = " << quantile(pack06, p)
@@ -375,34 +490,46 @@
 << " is " << cdf(complement(pack06, minimum_weight)) << endl;
// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.06 is 0.95221</pre>

- 
+ 

- Now we are getting really close, but to do the job properly, we might
- need to use root finding method, for example the tools provided, and
- used elsewhere, in the Math Toolkit, see <a class="link" href="../../../../toolkit/internals1/roots2.html" title="Root Finding Without Derivatives: Bisection, Bracket and TOMS748">Root
- Finding Without Derivatives</a>.
- 
+ 

- But in this (normal) distribution case, we can and should be even smarter
- and make a direct calculation.
- 
+ Now we are getting really close, but to do the job properly, we might
+ need to use root finding method, for example the tools provided,
+ and used elsewhere, in the Math Toolkit, see <a class="link" href="../../../../toolkit/internals1/roots2.html" title="Root Finding Without Derivatives: Bisection, Bracket and TOMS748">Root
+ Finding Without Derivatives</a>.
+ 

- Our required limit is minimum_weight = 2.9 kg, often called the random
- variate z. For a standard normal distribution, then probability p =
- N((minimum_weight - mean) / sd).
- 
+ 

- We want to find the standard deviation that would be required to meet
- this limit, so that the p th quantile is located at z (minimum_weight).
- In this case, the 0.05 (5%) quantile is at 2.9 kg pack weight, when
- the mean is 3 kg, ensuring that 0.95 (95%) of packs are above the minimum
- weight.
- 
+ But in this (normal) distribution case, we can and should be even
+ smarter and make a direct calculation.
+ 

- Rearranging, we can directly calculate the required standard deviation:
- 
+ 

-
+ Our required limit is minimum_weight = 2.9 kg, often called the random
+ variate z. For a standard normal distribution, then probability p
+ = N((minimum_weight - mean) / sd).
+ 
+
+ 
+
+ We want to find the standard deviation that would be required to
+ meet this limit, so that the p th quantile is located at z (minimum_weight).
+ In this case, the 0.05 (5%) quantile is at 2.9 kg pack weight, when
+ the mean is 3 kg, ensuring that 0.95 (95%) of packs are above the
+ minimum weight.
+ 
+
+ 
+
+ Rearranging, we can directly calculate the required standard deviation:
+ 
+
+ 
+
+

<pre class="programlisting">normal N01; // standard normal distribution with meamn zero and unit standard deviation.
p = 0.05;
@@ -413,13 +540,17 @@
 << minimum_weight << ", would need a standard deviation of " << sd95 << endl;
// For the 0.05th quantile to be located at 2.9, would need a standard deviation of 0.0607957</pre>

- 
+ 

- We can now construct a new (normal) distribution pack95 for the 'better'
- packer, and check that our distribution will meet the specification.
- 
+ 

-
+ We can now construct a new (normal) distribution pack95 for the 'better'
+ packer, and check that our distribution will meet the specification.
+ 
+
+ 
+
+

<pre class="programlisting">normal pack95(mean, sd95);
cout <<"Fraction of packs >= " << minimum_weight << " with a mean of " << mean
@@ -427,75 +558,108 @@
 << " is " << cdf(complement(pack95, minimum_weight)) << endl;
// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.0607957 is 0.95</pre>

- 
+ 

- This calculation is generalized in the free function find_scale, as
- shown below, giving the same standard deviation.
- 
+ 

-
+ This calculation is generalized in the free function find_scale,
+ as shown below, giving the same standard deviation.
+ 
+
+ 
+
+

<pre class="programlisting">double ss = find_scale<normal>(minimum_weight, under_fraction, packs.mean());
cout << "find_scale<normal>(minimum_weight, under_fraction, packs.mean()); " << ss << endl;
// find_scale<normal>(minimum_weight, under_fraction, packs.mean()); 0.0607957</pre>

- 
+ 

- If we had defined an over_fraction, or percentage that must pass specification
- 
+ 

-
+ If we had defined an over_fraction, or percentage that must pass
+ specification
+ 
+
+ 
+
+

<pre class="programlisting">double over_fraction = 0.95;</pre>

- 
+ 

- And (wrongly) written
- 
+ 
+
+ And (wrongly) written
+ 
+
+
+
<pre class="programlisting">double sso = find_scale<normal>(minimum_weight, over_fraction, packs.mean());
</pre>

- With the default policy, we would get a message like
- 
+ 
+
+ With the default policy, we would get a message like
+ 
+
+
+
<pre class="programlisting">Message from thrown exception was:
 Error in function boost::math::find_scale<Dist, Policy>(double, double, double, Policy):
 Computed scale (-0.060795683191176959) is <= 0! Was the complement intended?
</pre>

- But this would return a negative standard
- deviation - obviously impossible. The probability should be 1 - over_fraction,
- not over_fraction, thus:
- 
+ 

-
+ But this would return a negative
+ standard deviation - obviously impossible. The probability should
+ be 1 - over_fraction, not over_fraction, thus:
+ 
+
+ 
+
+

<pre class="programlisting">double ss1o = find_scale<normal>(minimum_weight, 1 - over_fraction, packs.mean());
cout << "find_scale<normal>(minimum_weight, under_fraction, packs.mean()); " << ss1o << endl;
// find_scale<normal>(minimum_weight, under_fraction, packs.mean()); 0.0607957</pre>

- 
+ 

- But notice that using '1 - over_fraction' - will lead to a <a class="link" href="../../overview/complements.html#why_complements">loss
- of accuracy, especially if over_fraction was close to unity.</a>
- In this (very common) case, we should instead use the <a class="link" href="../../overview.html#complements">complements</a>,
- giving the most accurate result.
- 
+ 

-
+ But notice that using '1 - over_fraction' - will lead to a <a class="link" href="../../overview/complements.html#why_complements">loss of accuracy, especially if over_fraction
+ was close to unity.</a> In this (very common) case, we should
+ instead use the <a class="link" href="../../overview.html#complements">complements</a>, giving
+ the most accurate result.
+ 
+
+ 
+
+

<pre class="programlisting">double ssc = find_scale<normal>(complement(minimum_weight, over_fraction, packs.mean()));
cout << "find_scale<normal>(complement(minimum_weight, over_fraction, packs.mean())); " << ssc << endl;
// find_scale<normal>(complement(minimum_weight, over_fraction, packs.mean())); 0.0607957</pre>

- 
+ 

- Note that our guess of 0.06 was close to the accurate value of 0.060795683191176959.
- 
+ 

- We can again confirm our prediction thus:
- 
+ Note that our guess of 0.06 was close to the accurate value of 0.060795683191176959.
+ 

-
+ 
+
+ We can again confirm our prediction thus:
+ 
+
+ 
+
+

<pre class="programlisting">normal pack95c(mean, ssc);
cout <<"Fraction of packs >= " << minimum_weight << " with a mean of " << mean
@@ -503,31 +667,45 @@
 << " is " << cdf(complement(pack95c, minimum_weight)) << endl;
// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.0607957 is 0.95</pre>

- 
+ 

- Notice that these two deceptively simple questions:
- 
+ 
+
+ Notice that these two deceptively simple questions:
+ 
+
+ 
<div class="itemizedlist"><ul type="disc"><li>
- Do we over-fill to make sure we meet a minimum specification (or
- under-fill to avoid an overdose)?
- </li></ul></div>
+ Do we over-fill to make sure we meet a minimum specification
+ (or under-fill to avoid an overdose)?
+ </li></ul></div>

- and/or
- 
+ 
+
+ and/or
+ 
+
+ 
<div class="itemizedlist"><ul type="disc"><li>
- Do we measure better?
- </li></ul></div>
+ Do we measure better?
+ </li></ul></div>

- are actually extremely common.
- 
+ 

- The weight of beef might be replaced by a measurement of more or less
- anything, from drug tablet content, Apollo landing rocket firing, X-ray
- treatment doses...
- 
+ are actually extremely common.
+ 

- The scale can be variation in dispensing or uncertainty in measurement.
- 
+ 
+
+ The weight of beef might be replaced by a measurement of more or
+ less anything, from drug tablet content, Apollo landing rocket firing,
+ X-ray treatment doses...
+ 
+
+ 
+
+ The scale can be variation in dispensing or uncertainty in measurement.
+ 

 See find_mean_and_sd_normal.cpp
 for full source code & appended program output.

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,16 +24,20 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h6 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_scale_eg"></a><a class="link" href="find_scale_eg.html" title="Find Scale (Standard Deviation) Example">Find
- Scale (Standard Deviation) Example</a>
+<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_scale_eg"></a><a class="link" href="find_scale_eg.html" title="Find Scale (Standard Deviation) Example">
+ Find Scale (Standard Deviation) Example</a>
</h6></div></div></div>

- First we need some includes to access the <a class="link" href="../../../dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal
- Distribution</a>, the algorithms to find scale (and some std output
- of course).
- 
+ 

-
+ First we need some includes to access the <a class="link" href="../../../dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal
+ Distribution</a>, the algorithms to find scale (and some std output
+ of course).
+ 
+
+ 
+
+

<pre class="programlisting">#include <boost/math/distributions/normal.hpp> // for normal_distribution
 using boost::math::normal; // typedef provides default type is double.
@@ -50,27 +54,35 @@
 using std::numeric_limits;
</pre>

- 
+ 

- For this example, we will use the standard <a class="link" href="../../../dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal
- Distribution</a>, with location (mean) zero and standard deviation
- (scale) unity. Conveniently, this is also the default for this implementation's
- constructor.
- 
+ 

-
+ For this example, we will use the standard <a class="link" href="../../../dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal
+ Distribution</a>, with location (mean) zero and standard deviation
+ (scale) unity. Conveniently, this is also the default for this implementation's
+ constructor.
+ 
+
+ 
+
+

<pre class="programlisting">normal N01; // Default 'standard' normal distribution with zero mean
double sd = 1.; // and standard deviation is 1.</pre>

- 
+ 

- Suppose we want to find a different normal distribution with standard
- deviation so that only fraction p (here 0.001 or 0.1%) are below a
- certain chosen limit (here -2. standard deviations).
- 
+ 

-
+ Suppose we want to find a different normal distribution with standard
+ deviation so that only fraction p (here 0.001 or 0.1%) are below
+ a certain chosen limit (here -2. standard deviations).
+ 
+
+ 
+
+

<pre class="programlisting">double z = -2.; // z to give prob p
double p = 0.001; // only 0.1% below z = -2
@@ -84,46 +96,70 @@
 << ", has " << "fraction > " << z
 << ", p = " << cdf(complement(N01, z)) << endl; // Note: uses complement.</pre>

- 
+ 
+
+
+
<pre class="programlisting">Normal distribution with mean = 0 has fraction <= -2, p = 0.0227501
Normal distribution with mean = 0 has fraction > -2, p = 0.97725
</pre>

- Noting that p = 0.02 instead of our target of 0.001, we can now use
- <code class="computeroutput">find_scale</code> to give
- a new standard deviation.
- 
+ 

-
+ Noting that p = 0.02 instead of our target of 0.001, we can now use
+ <code class="computeroutput">find_scale</code> to give
+ a new standard deviation.
+ 
+
+ 
+
+

<pre class="programlisting">double l = N01.location();
double s = find_scale<normal>(z, p, l);
cout << "scale (standard deviation) = " << s << endl;</pre>

- 
+ 

- that outputs:
- 
+ 
+
+ that outputs:
+ 
+
+
+
<pre class="programlisting">scale (standard deviation) = 0.647201
</pre>

- showing that we need to reduce the standard deviation from 1. to 0.65.
- 
+ 

- Then we can check that we have achieved our objective by constructing
- a new distribution with the new standard deviation (but same zero mean):
- 
+ showing that we need to reduce the standard deviation from 1. to
+ 0.65.
+ 

-
+ 
+
+ Then we can check that we have achieved our objective by constructing
+ a new distribution with the new standard deviation (but same zero
+ mean):
+ 
+
+ 
+
+

<pre class="programlisting">normal np001pc(N01.location(), s);</pre>

- 
+ 

- And re-calculating the fraction below (and above) our chosen limit.
- 
+ 

-
+ And re-calculating the fraction below (and above) our chosen limit.
+ 
+
+ 
+
+

<pre class="programlisting">cout << "Normal distribution with mean = " << l
 << " has " << "fraction <= " << z
@@ -132,37 +168,53 @@
 << " has " << "fraction > " << z
 << ", p = " << cdf(complement(np001pc, z)) << endl;</pre>

- 
+ 
+
+
+
<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="id967664"></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
- how Errors from find_scale are handled</a>
- </h5>
-
- We can also control the policy for handling various errors. For example,
- we can define a new (possibly unwise) policy to ignore domain errors
- ('bad' arguments).
- 

- Unless we are using the boost::math namespace, we will need:
- 
+ <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="id1078521"></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
+ how Errors from find_scale are handled</a>
+ </h5>

-
+ 
+
+ We can also control the policy for handling various errors. For example,
+ we can define a new (possibly unwise) policy to ignore domain errors
+ ('bad' arguments).
+ 
+
+ 
+
+ Unless we are using the boost::math namespace, we will need:
+ 
+
+ 
+
+

<pre class="programlisting">using boost::math::policies::policy;
using boost::math::policies::domain_error;
using boost::math::policies::ignore_error;</pre>

- 
+ 

- Using a typedef is convenient, especially if it is re-used, although
- it is not required, as the various examples below show.
- 
+ 

-
+ Using a typedef is convenient, especially if it is re-used, although
+ it is not required, as the various examples below show.
+ 
+
+ 
+
+

<pre class="programlisting">typedef policy<domain_error<ignore_error> > ignore_domain_policy;
// find_scale with new policy, using typedef.
@@ -175,16 +227,20 @@
// New policy, without typedef.
l = find_scale<normal>(z, p, l, policy<domain_error<ignore_error> >());</pre>

- 
+ 

- If we want to express a probability, say 0.999, that is a complement,
- <code class="computeroutput">1 -
- p</code> we should not even think
- of writing <code class="computeroutput">find_scale<normal>(z, 1 - p, l)</code>, but <a class="link" href="../../overview/complements.html#why_complements">instead</a>,
- use the <a class="link" href="../../overview.html#complements">complements</a> version.
- 
+ 

-
+ If we want to express a probability, say 0.999, that is a complement,
+ <code class="computeroutput">1 -
+ p</code> we should not even think
+ of writing <code class="computeroutput">find_scale<normal>(z, 1 - p, l)</code>, but <a class="link" href="../../overview/complements.html#why_complements">instead</a>,
+ use the <a class="link" href="../../overview.html#complements">complements</a> version.
+ 
+
+ 
+
+

<pre class="programlisting">z = -2.;
double q = 0.999; // = 1 - p; // complement of 0.001.
@@ -196,24 +252,31 @@
cout << "Normal distribution with mean = " << l << " has "
 << "fraction > " << z << " = " << cdf(complement(np95pc, z)) << endl;</pre>

- 
+ 

- Sadly, it is all too easy to get probabilities the wrong way round,
- when you may get a warning like this:
- 
+ 
+
+ Sadly, it is all too easy to get probabilities the wrong way round,
+ when you may get a warning like this:
+ 
+
+
+
<pre class="programlisting">Message from thrown exception was:
 Error in function boost::math::find_scale<Dist, Policy>(complement(double, double, double, Policy)):
 Computed scale (-0.48043523852179076) is <= 0! Was the complement intended?
</pre>

- The default error handling policy is to throw an exception with this
- message, but if you chose a policy to ignore the error, the (impossible)
- negative scale is quietly returned.
- 
+ 
+
+ The default error handling policy is to throw an exception with this
+ message, but if you chose a policy to ignore the error, the (impossible)
+ negative scale is quietly returned.
+ 

 See find_scale_example.cpp
- for full source code: the program output looks like this:
- 
+ for full source code: the program output looks like this:
+
<pre class="programlisting">Example: Find scale (standard deviation).
Normal distribution with mean = 0, standard deviation 1, has fraction <= -2, p = 0.0227501
Normal distribution with mean = 0, standard deviation 1, has fraction > -2, p = 0.97725
@@ -223,6 +286,8 @@
Normal distribution with mean = 0.946339 has fraction <= -2 = 0.001
Normal distribution with mean = 0.946339 has fraction > -2 = 0.999
</pre>
+
+ 
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nag_library.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nag_library.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nag_library.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,7 +24,7 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.nag_library"></a><a class="link" href="nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions">Comparison
+<a name="math_toolkit.dist.stat_tut.weg.nag_library"></a><a class="link" href="nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions"> Comparison
with C, R, FORTRAN-style Free Functions</a>
</h5></div></div></div>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,11 +24,11 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.nccs_eg"></a><a class="link" href="nccs_eg.html" title="Non Central Chi Squared Example">Non Central
+<a name="math_toolkit.dist.stat_tut.weg.nccs_eg"></a><a class="link" href="nccs_eg.html" title="Non Central Chi Squared Example"> Non Central
 Chi Squared Example</a>
</h5></div></div></div>
-<div class="toc"><dl><dt><a href="nccs_eg/nccs_power_eg.html">Tables
- of the power function of the χ2 test.</a></dt></dl></div>
+<div class="toc"><dl><dt><a href="nccs_eg/nccs_power_eg.html">
+ Tables of the power function of the χ2 test.</a></dt></dl></div>

 (See also the reference documentation for the <a class="link" href="../../dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral
 Chi Squared Distribution</a>.)

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,23 +24,29 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h6 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.nccs_eg.nccs_power_eg"></a><a class="link" href="nccs_power_eg.html" title="Tables of the power function of the χ2 test.">Tables
- of the power function of the χ2 test.</a>
+<a name="math_toolkit.dist.stat_tut.weg.nccs_eg.nccs_power_eg"></a><a class="link" href="nccs_power_eg.html" title="Tables of the power function of the χ2 test.">
+ Tables of the power function of the χ2 test.</a>
</h6></div></div></div>

- This example computes a table of the power of the χ2
-test at the 5% significance
- level, for various degrees of freedom and non-centrality parameters.
- The table is deliberately the same as Table 6 from "The Non-Central
- χ2 and F-Distributions and their applications.", P. B. Patnaik,
- Biometrika, Vol. 36, No. 1/2 (June 1949), 202-232.
- 
+ 

- First we need some includes to access the non-central chi squared distribution
- (and some basic std output of course).
- 
+ This example computes a table of the power of the χ2
+test at the 5%
+ significance level, for various degrees of freedom and non-centrality
+ parameters. The table is deliberately the same as Table 6 from "The
+ Non-Central χ2 and F-Distributions and their applications.", P.
+ B. Patnaik, Biometrika, Vol. 36, No. 1/2 (June 1949), 202-232.
+ 
+
+ 
+
+ First we need some includes to access the non-central chi squared
+ distribution (and some basic std output of course).
+ 
+
+ 

-
+

<pre class="programlisting">#include <boost/math/distributions/non_central_chi_squared.hpp>
using boost::math::chi_squared;
@@ -53,13 +59,17 @@
int main()
{</pre>

- 
+ 

- Create a table of the power of the χ2 test at 5% significance level,
- start with a table header:
- 
+ 
+
+ Create a table of the power of the χ2 test at 5% significance level,
+ start with a table header:
+ 
+
+ 

-
+

<pre class="programlisting">cout << "[table\n[[[nu]]";
for(int lam = 2; lam <= 20; lam += 2)
@@ -68,16 +78,22 @@
}
cout << "]\n";</pre>

- 
+ 

- (Note: the enclosing [] brackets are to format as a table in Boost.Quickbook).
- 
+ 

- Enumerate the rows and columns and print the power of the test for
- each table cell:
- 
+ (Note: the enclosing [] brackets are to format as a table in Boost.Quickbook).
+ 
+
+ 
+
+ Enumerate the rows and columns and print the power of the test for
+ each table cell:
+ 

-
+ 
+
+

<pre class="programlisting">for(int n = 2; n <= 20; ++n)
{
@@ -85,31 +101,43 @@
 for(int lam = 2; lam <= 20; lam += 2)
 {</pre>

- 
+ 

- Calculate the χ2 statistic for a 5% significance:
- 
+ 
+
+ Calculate the χ2 statistic for a 5% significance:
+ 

-
+ 
+
+

<pre class="programlisting">double cs = quantile(complement(chi_squared(n), 0.05));</pre>

- 
+ 

- The power of the test is given by the complement of the CDF of the
- non-central χ2 distribution:
- 
+ 
+
+ The power of the test is given by the complement of the CDF of the
+ non-central χ2 distribution:
+ 
+
+ 

-
+

<pre class="programlisting">double beta = cdf(complement(non_central_chi_squared(n, lam), cs));</pre>

- 
+ 

- Then output the cell value:
- 
+ 
+
+ Then output the cell value:
+ 
+
+ 

-
+

<pre class="programlisting"> cout << "[" << setprecision(3) << beta << "]";
 }
@@ -118,18 +146,24 @@
 cout << "]" << endl;
}</pre>

- 
+ 

- The output from this program is a table in Boost.Quickbook format as
- shown below.
- 
+ 

- We can interpret this as follows - for example if ν=10 and λ=10 then
- the power of the test is 0.542 - so we have only a 54% chance of correctly
- detecting that our null hypothesis is false, and a 46% chance of incurring
- a type II error (failing to reject the null hypothesis when it is in
- fact false):
- 
+ The output from this program is a table in Boost.Quickbook format
+ as shown below.
+ 
+
+ 
+
+ We can interpret this as follows - for example if ν=10 and λ=10 then
+ the power of the test is 0.542 - so we have only a 54% chance of
+ correctly detecting that our null hypothesis is false, and a 46%
+ chance of incurring a type II error (failing to reject the null hypothesis
+ when it is in fact false):
+ 
+
+ 
<div class="informaltable"><table class="table">
<colgroup>
<col>
@@ -146,1150 +180,1154 @@
</colgroup>
<thead><tr>
<th>
- 
- ν
- 
- </th>
+ 
+ ν
+ 
+ </th>
<th>
- 
- λ=2
- 
- </th>
+ 
+ λ=2
+ 
+ </th>
<th>
- 
- λ=4
- 
- </th>
+ 
+ λ=4
+ 
+ </th>
<th>
- 
- λ=6
- 
- </th>
+ 
+ λ=6
+ 
+ </th>
<th>
- 
- λ=8
- 
- </th>
+ 
+ λ=8
+ 
+ </th>
<th>
- 
- λ=10
- 
- </th>
+ 
+ λ=10
+ 
+ </th>
<th>
- 
- λ=12
- 
- </th>
+ 
+ λ=12
+ 
+ </th>
<th>
- 
- λ=14
- 
- </th>
+ 
+ λ=14
+ 
+ </th>
<th>
- 
- λ=16
- 
- </th>
+ 
+ λ=16
+ 
+ </th>
<th>
- 
- λ=18
- 
- </th>
+ 
+ λ=18
+ 
+ </th>
<th>
- 
- λ=20
- 
- </th>
+ 
+ λ=20
+ 
+ </th>
</tr></thead>
<tbody>
<tr>
<td>
- 
- 2
- 
- </td>
-<td>
- 
- 0.226
- 
- </td>
-<td>
- 
- 0.415
- 
- </td>
-<td>
- 
- 0.584
- 
- </td>
-<td>
- 
- 0.718
- 
- </td>
-<td>
- 
- 0.815
- 
- </td>
-<td>
- 
- 0.883
- 
- </td>
-<td>
- 
- 0.928
- 
- </td>
-<td>
- 
- 0.957
- 
- </td>
-<td>
- 
- 0.974
- 
- </td>
-<td>
- 
- 0.985
- 
- </td>
+ 
+ 2
+ 
+ </td>
+<td>
+ 
+ 0.226
+ 
+ </td>
+<td>
+ 
+ 0.415
+ 
+ </td>
+<td>
+ 
+ 0.584
+ 
+ </td>
+<td>
+ 
+ 0.718
+ 
+ </td>
+<td>
+ 
+ 0.815
+ 
+ </td>
+<td>
+ 
+ 0.883
+ 
+ </td>
+<td>
+ 
+ 0.928
+ 
+ </td>
+<td>
+ 
+ 0.957
+ 
+ </td>
+<td>
+ 
+ 0.974
+ 
+ </td>
+<td>
+ 
+ 0.985
+ 
+ </td>
</tr>
<tr>
<td>
- 
- 3
- 
- </td>
-<td>
- 
- 0.192
- 
- </td>
-<td>
- 
- 0.359
- 
- </td>
-<td>
- 
- 0.518
- 
- </td>
-<td>
- 
- 0.654
- 
- </td>
-<td>
- 
- 0.761
- 
- </td>
-<td>
- 
- 0.84
- 
- </td>
-<td>
- 
- 0.896
- 
- </td>
-<td>
- 
- 0.934
- 
- </td>
-<td>
- 
- 0.959
- 
- </td>
-<td>
- 
- 0.975
- 
- </td>
+ 
+ 3
+ 
+ </td>
+<td>
+ 
+ 0.192
+ 
+ </td>
+<td>
+ 
+ 0.359
+ 
+ </td>
+<td>
+ 
+ 0.518
+ 
+ </td>
+<td>
+ 
+ 0.654
+ 
+ </td>
+<td>
+ 
+ 0.761
+ 
+ </td>
+<td>
+ 
+ 0.84
+ 
+ </td>
+<td>
+ 
+ 0.896
+ 
+ </td>
+<td>
+ 
+ 0.934
+ 
+ </td>
+<td>
+ 
+ 0.959
+ 
+ </td>
+<td>
+ 
+ 0.975
+ 
+ </td>
</tr>
<tr>
<td>
- 
- 4
- 
- </td>
-<td>
- 
- 0.171
- 
- </td>
-<td>
- 
- 0.32
- 
- </td>
-<td>
- 
- 0.47
- 
- </td>
-<td>
- 
- 0.605
- 
- </td>
-<td>
- 
- 0.716
- 
- </td>
-<td>
- 
- 0.802
- 
- </td>
-<td>
- 
- 0.866
- 
- </td>
-<td>
- 
- 0.912
- 
- </td>
-<td>
- 
- 0.943
- 
- </td>
-<td>
- 
- 0.964
- 
- </td>
+ 
+ 4
+ 
+ </td>
+<td>
+ 
+ 0.171
+ 
+ </td>
+<td>
+ 
+ 0.32
+ 
+ </td>
+<td>
+ 
+ 0.47
+ 
+ </td>
+<td>
+ 
+ 0.605
+ 
+ </td>
+<td>
+ 
+ 0.716
+ 
+ </td>
+<td>
+ 
+ 0.802
+ 
+ </td>
+<td>
+ 
+ 0.866
+ 
+ </td>
+<td>
+ 
+ 0.912
+ 
+ </td>
+<td>
+ 
+ 0.943
+ 
+ </td>
+<td>
+ 
+ 0.964
+ 
+ </td>
</tr>
<tr>
<td>
- 
- 5
- 
- </td>
-<td>
- 
- 0.157
- 
- </td>
-<td>
- 
- 0.292
- 
- </td>
-<td>
- 
- 0.433
- 
- </td>
-<td>
- 
- 0.564
- 
- </td>
-<td>
- 
- 0.677
- 
- </td>
-<td>
- 
- 0.769
- 
- </td>
-<td>
- 
- 0.839
- 
- </td>
-<td>
- 
- 0.89
- 
- </td>
-<td>
- 
- 0.927
- 
- </td>
-<td>
- 
- 0.952
- 
- </td>
+ 
+ 5
+ 
+ </td>
+<td>
+ 
+ 0.157
+ 
+ </td>
+<td>
+ 
+ 0.292
+ 
+ </td>
+<td>
+ 
+ 0.433
+ 
+ </td>
+<td>
+ 
+ 0.564
+ 
+ </td>
+<td>
+ 
+ 0.677
+ 
+ </td>
+<td>
+ 
+ 0.769
+ 
+ </td>
+<td>
+ 
+ 0.839
+ 
+ </td>
+<td>
+ 
+ 0.89
+ 
+ </td>
+<td>
+ 
+ 0.927
+ 
+ </td>
+<td>
+ 
+ 0.952
+ 
+ </td>
</tr>
<tr>
<td>
- 
- 6
- 
- </td>
-<td>
- 
- 0.146
- 
- </td>
-<td>
- 
- 0.27
- 
- </td>
-<td>
- 
- 0.403
- 
- </td>
-<td>
- 
- 0.531
- 
- </td>
-<td>
- 
- 0.644
- 
- </td>
-<td>
- 
- 0.738
- 
- </td>
-<td>
- 
- 0.813
- 
- </td>
-<td>
- 
- 0.869
- 
- </td>
-<td>
- 
- 0.911
- 
- </td>
-<td>
- 
- 0.94
- 
- </td>
+ 
+ 6
+ 
+ </td>
+<td>
+ 
+ 0.146
+ 
+ </td>
+<td>
+ 
+ 0.27
+ 
+ </td>
+<td>
+ 
+ 0.403
+ 
+ </td>
+<td>
+ 
+ 0.531
+ 
+ </td>
+<td>
+ 
+ 0.644
+ 
+ </td>
+<td>
+ 
+ 0.738
+ 
+ </td>
+<td>
+ 
+ 0.813
+ 
+ </td>
+<td>
+ 
+ 0.869
+ 
+ </td>
+<td>
+ 
+ 0.911
+ 
+ </td>
+<td>
+ 
+ 0.94
+ 
+ </td>
</tr>
<tr>
<td>
- 
- 7
- 
- </td>
-<td>
- 
- 0.138
- 
- </td>
-<td>
- 
- 0.252
- 
- </td>
-<td>
- 
- 0.378
- 
- </td>
-<td>
- 
- 0.502
- 
- </td>
-<td>
- 
- 0.614
- 
- </td>
-<td>
- 
- 0.71
- 
- </td>
-<td>
- 
- 0.788
- 
- </td>
-<td>
- 
- 0.849
- 
- </td>
-<td>
- 
- 0.895
- 
- </td>
-<td>
- 
- 0.928
- 
- </td>
+ 
+ 7
+ 
+ </td>
+<td>
+ 
+ 0.138
+ 
+ </td>
+<td>
+ 
+ 0.252
+ 
+ </td>
+<td>
+ 
+ 0.378
+ 
+ </td>
+<td>
+ 
+ 0.502
+ 
+ </td>
+<td>
+ 
+ 0.614
+ 
+ </td>
+<td>
+ 
+ 0.71
+ 
+ </td>
+<td>
+ 
+ 0.788
+ 
+ </td>
+<td>
+ 
+ 0.849
+ 
+ </td>
+<td>
+ 
+ 0.895
+ 
+ </td>
+<td>
+ 
+ 0.928
+ 
+ </td>
</tr>
<tr>
<td>
- 
- 8
- 
- </td>
-<td>
- 
- 0.131
- 
- </td>
-<td>
- 
- 0.238
- 
- </td>
-<td>
- 
- 0.357
- 
- </td>
-<td>
- 
- 0.477
- 
- </td>
-<td>
- 
- 0.588
- 
- </td>
-<td>
- 
- 0.685
- 
- </td>
-<td>
- 
- 0.765
- 
- </td>
-<td>
- 
- 0.829
- 
- </td>
-<td>
- 
- 0.879
- 
- </td>
-<td>
- 
- 0.915
- 
- </td>
+ 
+ 8
+ 
+ </td>
+<td>
+ 
+ 0.131
+ 
+ </td>
+<td>
+ 
+ 0.238
+ 
+ </td>
+<td>
+ 
+ 0.357
+ 
+ </td>
+<td>
+ 
+ 0.477
+ 
+ </td>
+<td>
+ 
+ 0.588
+ 
+ </td>
+<td>
+ 
+ 0.685
+ 
+ </td>
+<td>
+ 
+ 0.765
+ 
+ </td>
+<td>
+ 
+ 0.829
+ 
+ </td>
+<td>
+ 
+ 0.879
+ 
+ </td>
+<td>
+ 
+ 0.915
+ 
+ </td>
</tr>
<tr>
<td>
- 
- 9
- 
- </td>
-<td>
- 
- 0.125
- 
- </td>
-<td>
- 
- 0.225
- 
- </td>
-<td>
- 
- 0.339
- 
- </td>
-<td>
- 
- 0.454
- 
- </td>
-<td>
- 
- 0.564
- 
- </td>
-<td>
- 
- 0.661
- 
- </td>
-<td>
- 
- 0.744
- 
- </td>
-<td>
- 
- 0.811
- 
- </td>
-<td>
- 
- 0.863
- 
- </td>
-<td>
- 
- 0.903
- 
- </td>
+ 
+ 9
+ 
+ </td>
+<td>
+ 
+ 0.125
+ 
+ </td>
+<td>
+ 
+ 0.225
+ 
+ </td>
+<td>
+ 
+ 0.339
+ 
+ </td>
+<td>
+ 
+ 0.454
+ 
+ </td>
+<td>
+ 
+ 0.564
+ 
+ </td>
+<td>
+ 
+ 0.661
+ 
+ </td>
+<td>
+ 
+ 0.744
+ 
+ </td>
+<td>
+ 
+ 0.811
+ 
+ </td>
+<td>
+ 
+ 0.863
+ 
+ </td>
+<td>
+ 
+ 0.903
+ 
+ </td>
</tr>
<tr>
<td>
- 
- 10
- 
- </td>
-<td>
- 
- 0.121
- 
- </td>
-<td>
- 
- 0.215
- 
- </td>
-<td>
- 
- 0.323
- 
- </td>
-<td>
- 
- 0.435
- 
- </td>
-<td>
- 
- 0.542
- 
- </td>
-<td>
- 
- 0.64
- 
- </td>
-<td>
- 
- 0.723
- 
- </td>
-<td>
- 
- 0.793
- 
- </td>
-<td>
- 
- 0.848
- 
- </td>
-<td>
- 
- 0.891
- 
- </td>
+ 
+ 10
+ 
+ </td>
+<td>
+ 
+ 0.121
+ 
+ </td>
+<td>
+ 
+ 0.215
+ 
+ </td>
+<td>
+ 
+ 0.323
+ 
+ </td>
+<td>
+ 
+ 0.435
+ 
+ </td>
+<td>
+ 
+ 0.542
+ 
+ </td>
+<td>
+ 
+ 0.64
+ 
+ </td>
+<td>
+ 
+ 0.723
+ 
+ </td>
+<td>
+ 
+ 0.793
+ 
+ </td>
+<td>
+ 
+ 0.848
+ 
+ </td>
+<td>
+ 
+ 0.891
+ 
+ </td>
</tr>
<tr>
<td>
- 
- 11
- 
- </td>
-<td>
- 
- 0.117
- 
- </td>
-<td>
- 
- 0.206
- 
- </td>
-<td>
- 
- 0.309
- 
- </td>
-<td>
- 
- 0.417
- 
- </td>
-<td>
- 
- 0.523
- 
- </td>
-<td>
- 
- 0.62
- 
- </td>
-<td>
- 
- 0.704
- 
- </td>
-<td>
- 
- 0.775
- 
- </td>
-<td>
- 
- 0.833
- 
- </td>
-<td>
- 
- 0.878
- 
- </td>
+ 
+ 11
+ 
+ </td>
+<td>
+ 
+ 0.117
+ 
+ </td>
+<td>
+ 
+ 0.206
+ 
+ </td>
+<td>
+ 
+ 0.309
+ 
+ </td>
+<td>
+ 
+ 0.417
+ 
+ </td>
+<td>
+ 
+ 0.523
+ 
+ </td>
+<td>
+ 
+ 0.62
+ 
+ </td>
+<td>
+ 
+ 0.704
+ 
+ </td>
+<td>
+ 
+ 0.775
+ 
+ </td>
+<td>
+ 
+ 0.833
+ 
+ </td>
+<td>
+ 
+ 0.878
+ 
+ </td>
</tr>
<tr>
<td>
- 
- 12
- 
- </td>
-<td>
- 
- 0.113
- 
- </td>
-<td>
- 
- 0.198
- 
- </td>
-<td>
- 
- 0.297
- 
- </td>
-<td>
- 
- 0.402
- 
- </td>
-<td>
- 
- 0.505
- 
- </td>
-<td>
- 
- 0.601
- 
- </td>
-<td>
- 
- 0.686
- 
- </td>
-<td>
- 
- 0.759
- 
- </td>
-<td>
- 
- 0.818
- 
- </td>
-<td>
- 
- 0.866
- 
- </td>
+ 
+ 12
+ 
+ </td>
+<td>
+ 
+ 0.113
+ 
+ </td>
+<td>
+ 
+ 0.198
+ 
+ </td>
+<td>
+ 
+ 0.297
+ 
+ </td>
+<td>
+ 
+ 0.402
+ 
+ </td>
+<td>
+ 
+ 0.505
+ 
+ </td>
+<td>
+ 
+ 0.601
+ 
+ </td>
+<td>
+ 
+ 0.686
+ 
+ </td>
+<td>
+ 
+ 0.759
+ 
+ </td>
+<td>
+ 
+ 0.818
+ 
+ </td>
+<td>
+ 
+ 0.866
+ 
+ </td>
</tr>
<tr>
<td>
- 
- 13
- 
- </td>
-<td>
- 
- 0.11
- 
- </td>
-<td>
- 
- 0.191
- 
- </td>
-<td>
- 
- 0.286
- 
- </td>
-<td>
- 
- 0.387
- 
- </td>
-<td>
- 
- 0.488
- 
- </td>
-<td>
- 
- 0.584
- 
- </td>
-<td>
- 
- 0.669
- 
- </td>
-<td>
- 
- 0.743
- 
- </td>
-<td>
- 
- 0.804
- 
- </td>
-<td>
- 
- 0.854
- 
- </td>
+ 
+ 13
+ 
+ </td>
+<td>
+ 
+ 0.11
+ 
+ </td>
+<td>
+ 
+ 0.191
+ 
+ </td>
+<td>
+ 
+ 0.286
+ 
+ </td>
+<td>
+ 
+ 0.387
+ 
+ </td>
+<td>
+ 
+ 0.488
+ 
+ </td>
+<td>
+ 
+ 0.584
+ 
+ </td>
+<td>
+ 
+ 0.669
+ 
+ </td>
+<td>
+ 
+ 0.743
+ 
+ </td>
+<td>
+ 
+ 0.804
+ 
+ </td>
+<td>
+ 
+ 0.854
+ 
+ </td>
</tr>
<tr>
<td>
- 
- 14
- 
- </td>
-<td>
- 
- 0.108
- 
- </td>
-<td>
- 
- 0.185
- 
- </td>
-<td>
- 
- 0.276
- 
- </td>
-<td>
- 
- 0.374
- 
- </td>
-<td>
- 
- 0.473
- 
- </td>
-<td>
- 
- 0.567
- 
- </td>
-<td>
- 
- 0.653
- 
- </td>
-<td>
- 
- 0.728
- 
- </td>
-<td>
- 
- 0.791
- 
- </td>
-<td>
- 
- 0.842
- 
- </td>
+ 
+ 14
+ 
+ </td>
+<td>
+ 
+ 0.108
+ 
+ </td>
+<td>
+ 
+ 0.185
+ 
+ </td>
+<td>
+ 
+ 0.276
+ 
+ </td>
+<td>
+ 
+ 0.374
+ 
+ </td>
+<td>
+ 
+ 0.473
+ 
+ </td>
+<td>
+ 
+ 0.567
+ 
+ </td>
+<td>
+ 
+ 0.653
+ 
+ </td>
+<td>
+ 
+ 0.728
+ 
+ </td>
+<td>
+ 
+ 0.791
+ 
+ </td>
+<td>
+ 
+ 0.842
+ 
+ </td>
</tr>
<tr>
<td>
- 
- 15
- 
- </td>
-<td>
- 
- 0.105
- 
- </td>
-<td>
- 
- 0.179
- 
- </td>
-<td>
- 
- 0.267
- 
- </td>
-<td>
- 
- 0.362
- 
- </td>
-<td>
- 
- 0.459
- 
- </td>
-<td>
- 
- 0.552
- 
- </td>
-<td>
- 
- 0.638
- 
- </td>
-<td>
- 
- 0.713
- 
- </td>
-<td>
- 
- 0.777
- 
- </td>
-<td>
- 
- 0.83
- 
- </td>
+ 
+ 15
+ 
+ </td>
+<td>
+ 
+ 0.105
+ 
+ </td>
+<td>
+ 
+ 0.179
+ 
+ </td>
+<td>
+ 
+ 0.267
+ 
+ </td>
+<td>
+ 
+ 0.362
+ 
+ </td>
+<td>
+ 
+ 0.459
+ 
+ </td>
+<td>
+ 
+ 0.552
+ 
+ </td>
+<td>
+ 
+ 0.638
+ 
+ </td>
+<td>
+ 
+ 0.713
+ 
+ </td>
+<td>
+ 
+ 0.777
+ 
+ </td>
+<td>
+ 
+ 0.83
+ 
+ </td>
</tr>
<tr>
<td>
- 
- 16
- 
- </td>
-<td>
- 
- 0.103
- 
- </td>
-<td>
- 
- 0.174
- 
- </td>
-<td>
- 
- 0.259
- 
- </td>
-<td>
- 
- 0.351
- 
- </td>
-<td>
- 
- 0.446
- 
- </td>
-<td>
- 
- 0.538
- 
- </td>
-<td>
- 
- 0.623
- 
- </td>
-<td>
- 
- 0.699
- 
- </td>
-<td>
- 
- 0.764
- 
- </td>
-<td>
- 
- 0.819
- 
- </td>
+ 
+ 16
+ 
+ </td>
+<td>
+ 
+ 0.103
+ 
+ </td>
+<td>
+ 
+ 0.174
+ 
+ </td>
+<td>
+ 
+ 0.259
+ 
+ </td>
+<td>
+ 
+ 0.351
+ 
+ </td>
+<td>
+ 
+ 0.446
+ 
+ </td>
+<td>
+ 
+ 0.538
+ 
+ </td>
+<td>
+ 
+ 0.623
+ 
+ </td>
+<td>
+ 
+ 0.699
+ 
+ </td>
+<td>
+ 
+ 0.764
+ 
+ </td>
+<td>
+ 
+ 0.819
+ 
+ </td>
</tr>
<tr>
<td>
- 
- 17
- 
- </td>
-<td>
- 
- 0.101
- 
- </td>
-<td>
- 
- 0.169
- 
- </td>
-<td>
- 
- 0.251
- 
- </td>
-<td>
- 
- 0.341
- 
- </td>
-<td>
- 
- 0.434
- 
- </td>
-<td>
- 
- 0.525
- 
- </td>
-<td>
- 
- 0.609
- 
- </td>
-<td>
- 
- 0.686
- 
- </td>
-<td>
- 
- 0.752
- 
- </td>
-<td>
- 
- 0.807
- 
- </td>
+ 
+ 17
+ 
+ </td>
+<td>
+ 
+ 0.101
+ 
+ </td>
+<td>
+ 
+ 0.169
+ 
+ </td>
+<td>
+ 
+ 0.251
+ 
+ </td>
+<td>
+ 
+ 0.341
+ 
+ </td>
+<td>
+ 
+ 0.434
+ 
+ </td>
+<td>
+ 
+ 0.525
+ 
+ </td>
+<td>
+ 
+ 0.609
+ 
+ </td>
+<td>
+ 
+ 0.686
+ 
+ </td>
+<td>
+ 
+ 0.752
+ 
+ </td>
+<td>
+ 
+ 0.807
+ 
+ </td>
</tr>
<tr>
<td>
- 
- 18
- 
- </td>
-<td>
- 
- 0.0992
- 
- </td>
-<td>
- 
- 0.165
- 
- </td>
-<td>
- 
- 0.244
- 
- </td>
-<td>
- 
- 0.332
- 
- </td>
-<td>
- 
- 0.423
- 
- </td>
-<td>
- 
- 0.512
- 
- </td>
-<td>
- 
- 0.596
- 
- </td>
-<td>
- 
- 0.673
- 
- </td>
-<td>
- 
- 0.74
- 
- </td>
-<td>
- 
- 0.796
- 
- </td>
+ 
+ 18
+ 
+ </td>
+<td>
+ 
+ 0.0992
+ 
+ </td>
+<td>
+ 
+ 0.165
+ 
+ </td>
+<td>
+ 
+ 0.244
+ 
+ </td>
+<td>
+ 
+ 0.332
+ 
+ </td>
+<td>
+ 
+ 0.423
+ 
+ </td>
+<td>
+ 
+ 0.512
+ 
+ </td>
+<td>
+ 
+ 0.596
+ 
+ </td>
+<td>
+ 
+ 0.673
+ 
+ </td>
+<td>
+ 
+ 0.74
+ 
+ </td>
+<td>
+ 
+ 0.796
+ 
+ </td>
</tr>
<tr>
<td>
- 
- 19
- 
- </td>
-<td>
- 
- 0.0976
- 
- </td>
-<td>
- 
- 0.161
- 
- </td>
-<td>
- 
- 0.238
- 
- </td>
-<td>
- 
- 0.323
- 
- </td>
-<td>
- 
- 0.412
- 
- </td>
-<td>
- 
- 0.5
- 
- </td>
-<td>
- 
- 0.584
- 
- </td>
-<td>
- 
- 0.66
- 
- </td>
-<td>
- 
- 0.728
- 
- </td>
-<td>
- 
- 0.786
- 
- </td>
+ 
+ 19
+ 
+ </td>
+<td>
+ 
+ 0.0976
+ 
+ </td>
+<td>
+ 
+ 0.161
+ 
+ </td>
+<td>
+ 
+ 0.238
+ 
+ </td>
+<td>
+ 
+ 0.323
+ 
+ </td>
+<td>
+ 
+ 0.412
+ 
+ </td>
+<td>
+ 
+ 0.5
+ 
+ </td>
+<td>
+ 
+ 0.584
+ 
+ </td>
+<td>
+ 
+ 0.66
+ 
+ </td>
+<td>
+ 
+ 0.728
+ 
+ </td>
+<td>
+ 
+ 0.786
+ 
+ </td>
</tr>
<tr>
<td>
- 
- 20
- 
- </td>
-<td>
- 
- 0.0961
- 
- </td>
-<td>
- 
- 0.158
- 
- </td>
-<td>
- 
- 0.232
- 
- </td>
-<td>
- 
- 0.315
- 
- </td>
-<td>
- 
- 0.402
- 
- </td>
-<td>
- 
- 0.489
- 
- </td>
-<td>
- 
- 0.572
- 
- </td>
-<td>
- 
- 0.648
- 
- </td>
-<td>
- 
- 0.716
- 
- </td>
-<td>
- 
- 0.775
- 
- </td>
+ 
+ 20
+ 
+ </td>
+<td>
+ 
+ 0.0961
+ 
+ </td>
+<td>
+ 
+ 0.158
+ 
+ </td>
+<td>
+ 
+ 0.232
+ 
+ </td>
+<td>
+ 
+ 0.315
+ 
+ </td>
+<td>
+ 
+ 0.402
+ 
+ </td>
+<td>
+ 
+ 0.489
+ 
+ </td>
+<td>
+ 
+ 0.572
+ 
+ </td>
+<td>
+ 
+ 0.648
+ 
+ </td>
+<td>
+ 
+ 0.716
+ 
+ </td>
+<td>
+ 
+ 0.775
+ 
+ </td>
</tr>
</tbody>
</table></div>

- See nc_chi_sq_example.cpp
- for the full C++ source code.
+ 
+
+ See nc_chi_sq_example.cpp
+ for the full C++ source code.
+ 
+
 
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg.html 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,19 +24,19 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.neg_binom_eg"></a><a class="link" href="neg_binom_eg.html" title="Negative Binomial Distribution Examples">Negative
+<a name="math_toolkit.dist.stat_tut.weg.neg_binom_eg"></a><a class="link" href="neg_binom_eg.html" title="Negative Binomial Distribution Examples"> Negative
Binomial Distribution Examples</a>
</h5></div></div></div>
<div class="toc"><dl>
-<dt><a href="neg_binom_eg/neg_binom_conf.html">Calculating
- Confidence Limits on the Frequency of Occurrence for the Negative Binomial
- Distribution</a></dt>
-<dt><a href="neg_binom_eg/neg_binom_size_eg.html">Estimating
- Sample Sizes for the Negative Binomial.</a></dt>
-<dt><a href="neg_binom_eg/negative_binomial_example1.html">Negative
- Binomial Sales Quota Example.</a></dt>
-<dt><a href="neg_binom_eg/negative_binomial_example2.html">Negative
- Binomial Table Printing Example.</a></dt>
+<dt><a href="neg_binom_eg/neg_binom_conf.html">
+ Calculating Confidence Limits on the Frequency of Occurrence for the
+ Negative Binomial Distribution</a></dt>
+<dt><a href="neg_binom_eg/neg_binom_size_eg.html">
+ Estimating Sample Sizes for the Negative Binomial.</a></dt>
+<dt><a href="neg_binom_eg/negative_binomial_example1.html">
+ Negative Binomial Sales Quota Example.</a></dt>
+<dt><a href="neg_binom_eg/negative_binomial_example2.html">
+ Negative Binomial Table Printing Example.</a></dt>
</dl></div>

(See also the reference documentation for the <a class="link" href="../../dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,9 +24,9 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h6 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.neg_binom_eg.neg_binom_conf"></a><a class="link" href="neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">Calculating
- Confidence Limits on the Frequency of Occurrence for the Negative Binomial
- Distribution</a>
+<a name="math_toolkit.dist.stat_tut.weg.neg_binom_eg.neg_binom_conf"></a><a class="link" href="neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">
+ Calculating Confidence Limits on the Frequency of Occurrence for the
+ Negative Binomial Distribution</a>
</h6></div></div></div>

 Imagine you have a process that follows a negative binomial distribution:
@@ -55,11 +55,15 @@
 illustrates their use.
 

- First we need some includes to access the negative binomial distribution
- (and some basic std output of course).
- 
+ 
+
+ First we need some includes to access the negative binomial distribution
+ (and some basic std output of course).
+ 
+
+ 

-
+

<pre class="programlisting">#include <boost/math/distributions/negative_binomial.hpp>
using boost::math::negative_binomial;
@@ -70,28 +74,39 @@
using std::setprecision;
using std::setw; using std::left; using std::fixed; using std::right;</pre>

- 
+ 

- First define a table of significance levels: these are the probabilities
- that the true occurrence frequency lies outside the calculated interval:
- 
+ 
+
+ First define a table of significance levels: these are the probabilities
+ that the true occurrence frequency lies outside the calculated interval:
+ 

-
+ 
+
+

<pre class="programlisting">double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };</pre>

- 
+ 

- Confidence value as % is (1 - alpha) * 100, so alpha 0.05 == 95% confidence
- that the true occurence frequency lies inside
- the calculated interval.
- 
+ 

- We need a function to calculate and print confidence limits for an
- observed frequency of occurrence that follows a negative binomial distribution.
- 
+ Confidence value as % is (1 - alpha) * 100, so alpha 0.05 == 95%
+ confidence that the true occurence frequency lies inside
+ the calculated interval.
+ 
+
+ 

-
+ We need a function to calculate and print confidence limits for an
+ observed frequency of occurrence that follows a negative binomial
+ distribution.
+ 
+
+ 
+
+

<pre class="programlisting">void confidence_limits_on_frequency(unsigned trials, unsigned successes)
{
@@ -117,21 +132,25 @@
 " Value (%) Limit Limit\n"
 "___________________________________________\n";</pre>

- 
+ 

- And now for the important part - the bounds themselves. For each value
- of alpha, we call <code class="computeroutput">find_lower_bound_on_p</code>
- and <code class="computeroutput">find_upper_bound_on_p</code>
- to obtain lower and upper bounds respectively. Note that since we are
- calculating a two-sided interval, we must divide the value of alpha
- in two. Had we been calculating a single-sided interval, for example:
- "Calculate a lower bound so that we are P% sure that
- the true occurrence frequency is greater than some value"
- then we would not have divided by
- two.
- 
+ 
+
+ And now for the important part - the bounds themselves. For each
+ value of alpha, we call <code class="computeroutput">find_lower_bound_on_p</code>
+ and <code class="computeroutput">find_upper_bound_on_p</code>
+ to obtain lower and upper bounds respectively. Note that since we
+ are calculating a two-sided interval, we must divide the value of
+ alpha in two. Had we been calculating a single-sided interval, for
+ example: "Calculate a lower bound so that we are P%
+ sure that the true occurrence frequency is greater than some value"
+ then we would not have divided by
+ two.
+ 
+
+ 

-
+

<pre class="programlisting"> // Now print out the upper and lower limits for the alpha table values.
 for(unsigned i = 0; i < sizeof(alpha)/sizeof(alpha[0]); ++i)
@@ -148,13 +167,17 @@
 cout << endl;
} // void confidence_limits_on_frequency(unsigned trials, unsigned successes)</pre>

- 
+ 

- And then call confidence_limits_on_frequency with increasing numbers
- of trials, but always the same success fraction 0.1, or 1 in 10.
- 
+ 
+
+ And then call confidence_limits_on_frequency with increasing numbers
+ of trials, but always the same success fraction 0.1, or 1 in 10.
+ 

-
+ 
+
+

<pre class="programlisting">int main()
{
@@ -167,7 +190,7 @@

</pre>

- 
+ 

 Let's see some sample output for a 1 in 10 success ratio, first for
 a mere 20 trials:

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h6 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.neg_binom_eg.neg_binom_size_eg"></a><a class="link" href="neg_binom_size_eg.html" title="Estimating Sample Sizes for the Negative Binomial.">Estimating
- Sample Sizes for the Negative Binomial.</a>
+<a name="math_toolkit.dist.stat_tut.weg.neg_binom_eg.neg_binom_size_eg"></a><a class="link" href="neg_binom_size_eg.html" title="Estimating Sample Sizes for the Negative Binomial.">
+ Estimating Sample Sizes for the Negative Binomial.</a>
</h6></div></div></div>

 Imagine you have an event (let's call it a "failure" - though
@@ -43,45 +43,64 @@
 demonstrates its usage.
 

- It centres around a routine that prints out a table of minimum sample
- sizes (number of trials) for various probability thresholds:
- 
+ 

-
+ It centres around a routine that prints out a table of minimum sample
+ sizes (number of trials) for various probability thresholds:
+ 
+
+ 
+
+

<pre class="programlisting">void find_number_of_trials(double failures, double p);</pre>

- 
+ 

- First define a table of significance levels: these are the maximum
- acceptable probability that failure or fewer events
- will be observed.
- 
+ 

-
+ First define a table of significance levels: these are the maximum
+ acceptable probability that failure or fewer
+ events will be observed.
+ 
+
+ 
+
+

<pre class="programlisting">double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };</pre>

- 
+ 

- Confidence value as % is (1 - alpha) * 100, so alpha 0.05 == 95% confidence
- that the desired number of failures will be observed. The values range
- from a very low 0.5 or 50% confidence up to an extremely high confidence
- of 99.999.
- 
+ 

- Much of the rest of the program is pretty-printing, the important part
- is in the calculation of minimum number of trials required for each
- value of alpha using:
- 
+ Confidence value as % is (1 - alpha) * 100, so alpha 0.05 == 95%
+ confidence that the desired number of failures will be observed.
+ The values range from a very low 0.5 or 50% confidence up to an extremely
+ high confidence of 99.999.
+ 
+
+ 
+
+ Much of the rest of the program is pretty-printing, the important
+ part is in the calculation of minimum number of trials required for
+ each value of alpha using:
+ 
+
+
+
<pre class="programlisting">(int)ceil(negative_binomial::find_minimum_number_of_trials(failures, p, alpha[i]);
</pre>

- find_minimum_number_of_trials returns a double, so <code class="computeroutput">ceil</code>
- rounds this up to ensure we have an integral minimum number of trials.
- 
+ 

-
+ find_minimum_number_of_trials returns a double, so <code class="computeroutput">ceil</code> rounds this up to ensure we
+ have an integral minimum number of trials.
+ 
+
+ 
+
+

<pre class="programlisting">
void find_number_of_trials(double failures, double p)
@@ -112,13 +131,17 @@
 cout << endl;
} // void find_number_of_trials(double failures, double p)</pre>

- 
+ 

- finally we can produce some tables of minimum trials for the chosen
- confidence levels:
- 
+ 

-
+ finally we can produce some tables of minimum trials for the chosen
+ confidence levels:
+ 
+
+ 
+
+

<pre class="programlisting">int main()
{
@@ -134,6 +157,8 @@

</pre>

+ 
+
 
<div class="note"><table border="0" summary="Note">
<tr>

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 2010-12-14 14:22:52 EST (Tue, 14 Dec 2010)
@@ -24,8 +24,8 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h6 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.neg_binom_eg.negative_binomial_example1"></a><a class="link" href="negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">Negative
- Binomial Sales Quota Example.</a>
+<a name="math_toolkit.dist.stat_tut.weg.neg_binom_eg.negative_binomial_example1"></a><a class="link" href="negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">
+ Negative Binomial Sales Quota Example.</a>
</h6></div></div></div>

 This example program <a href="../../../../../../../../example/negative_binomial_example1.cpp" target="_top">negative_binomial_example1.cpp
@@ -33,69 +33,92 @@
 of meeting a sales quota.
 

- Based on <a href="http://en.wikipedia.org/wiki/Negative_binomial_distribution" target="_top">a
- problem by Dr. Diane Evans, Professor of Mathematics at Rose-Hulman
- Institute of Technology</a>.
- 
-
- Pat is required to sell candy bars to raise money for the 6th grade
- field trip. There are thirty houses in the neighborhood, and Pat is
- not supposed to return home until five candy bars have been sold. So
- the child goes door to door, selling candy bars. At each house, there
- is a 0.4 probability (40%) of selling one candy bar and a 0.6 probability
- (60%) of selling nothing.
- 
-
- What is the probability mass (density) function (pdf) for selling the
- last (fifth) candy bar at the nth house?
- 
-
- The Negative Binomial(r, p) distribution describes the probability
- of k failures and r successes in k+r Bernoulli(p) trials with success
- on the last trial. (A <a href="http://en.wikipedia.org/wiki/Bernoulli_distribution" target="_top">Bernoulli
- trial</a> is one with only two possible outcomes, success of failure,
- and p is the probability of success). See also <a href="../../../../../" target="_top">http://en.wikipedia.org/wiki/Bernoulli_distribution
- Bernoulli distribution</a> and <a href="http://www.math.uah.edu/stat/bernoulli/Introduction.xhtml" target="_top">Bernoulli
- applications</a>.
- 
+ 

- In this example, we will deliberately produce a variety of calculations
- and outputs to demonstrate the ways that the negative binomial distribution
- can be implemented with this library: it is also deliberately over-commented.
- 
+ Based on <a href="http://en.wikipedia.org/wiki/Negative_binomial_distribution" target="_top">a
+ problem by Dr. Diane Evans, Professor of Mathematics at Rose-Hulman
+ Institute of Technology</a>.
+ 
+
+ 
+
+ Pat is required to sell candy bars to raise money for the 6th grade
+ field trip. There are thirty houses in the neighborhood, and Pat
+ is not supposed to return home until five candy bars have been sold.
+ So the child goes door to door, selling candy bars. At each house,
+ there is a 0.4 probability (40%) of selling one candy bar and a 0.6
+ probability (60%) of selling nothing.
+ 
+
+ 
+
+ What is the probability mass (density) function (pdf) for selling
+ the last (fifth) candy bar at the nth house?
+ 
+
+ 
+
+ The Negative Binomial(r, p) distribution describes the probability
+ of k failures and r successes in k+r Bernoulli(p) trials with success
+ on the last trial. (A <a href=&q