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Subject: [Boost-commit] svn:boost r67411 - in trunk/libs/math/doc/sf_and_dist: . html html/math_toolkit html/math_toolkit/backgrounders html/math_toolkit/dist html/math_toolkit/dist/dist_ref html/math_toolkit/dist/dist_ref/dists html/math_toolkit/dist/stat_tut html/math_toolkit/dist/stat_tut/overview html/math_toolkit/dist/stat_tut/weg html/math_toolkit/dist/stat_tut/weg/binom_eg html/math_toolkit/dist/stat_tut/weg/cs_eg html/math_toolkit/dist/stat_tut/weg/find_eg html/math_toolkit/dist/stat_tut/weg/nccs_eg html/math_toolkit/dist/stat_tut/weg/neg_binom_eg html/math_toolkit/dist/stat_tut/weg/normal_example html/math_toolkit/dist/stat_tut/weg/st_eg html/math_toolkit/extern_c html/math_toolkit/main_overview html/math_toolkit/perf html/math_toolkit/policy html/math_toolkit/policy/pol_ref html/math_toolkit/policy/pol_tutorial html/math_toolkit/special html/math_toolkit/special/bessel html/math_toolkit/special/ellint html/math_toolkit/special/expint html/math_toolkit/special/factorials html/math_toolkit/special/inv_hyper html/math_toolkit/special/powers html/math_toolkit/special/sf_beta html/math_toolkit/special/sf_erf html/math_toolkit/special/sf_gamma html/math_toolkit/special/sf_poly html/math_toolkit/special/sinc html/math_toolkit/special/zetas html/math_toolkit/status html/math_toolkit/toolkit html/math_toolkit/toolkit/internals1 html/math_toolkit/toolkit/internals2 html/math_toolkit/using_udt html/math_toolkit/utils html/math_toolkit/utils/next_float html/math_toolkit/utils/rounding
From: john_at_[hidden]
Date: 2010-12-22 05:23:21

Next message: eldiener_at_[hidden]: "[Boost-commit] svn:boost r67412 - sandbox/tti/libs/tti/test"
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Author: johnmaddock
Date: 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
New Revision: 67411
URL: http://svn.boost.org/trac/boost/changeset/67411

Log:
Fix typos in code examples for legendre polynomials and regenerate docs.
Text files modified:
   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 | 18
   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 | 182 +-
   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 | 20
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.html | 17
   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 | 263 +--
   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/geometric_eg.html | 609 ++++------
   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 | 71
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html | 511 +++-----
   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 | 393 ++----
   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 | 64
   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 | 39
   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 | 511 +++-----
   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 | 21
   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/doc/sf_and_dist/legendre.qbk | 16
   240 files changed, 6760 insertions(+), 9177 deletions(-)

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 2010-12-22 05:22:56 EST (Wed, 22 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="id876240"></a>
+<a name="id995297"></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)
 
@@ -64,445 +64,440 @@
<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 Distribution Examples</a></dt>
-<dt><a href="math_toolkit/dist/stat_tut/weg/cs_eg.html"> Chi Squared
+<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/f_eg.html"> F Distribution
+<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
 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/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/beta_dist.html">Beta
 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/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/extreme_dist.html"> Extreme
+<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
 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><a href="math_toolkit/dist/dist_ref/dists/pareto.html"> Pareto
+<dt>Pareto Distribution</dt>
+<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/poisson_dist.html"> Poisson
+<dt><a href="math_toolkit/dist/dist_ref/dists/rayleigh.html">Rayleigh
 Distribution</a></dt>
-<dt><a href="math_toolkit/dist/dist_ref/dists/rayleigh.html"> Rayleigh
+<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/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
+<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><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
+<dt>Error Functions</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
+<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>
-<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><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>
+<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>
</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 17, 2010 at 16:20:58 GMT</td>
+<td align="left">Last revised: December 22, 2010 at 10:15:07 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 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,16 +24,15 @@
</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><a href="backgrounders/relative_error.html"> Relative
- Error</a></dt>
-<dt> The Lanczos Approximation</dt>
-<dt> The Remez Method</dt>
-<dt> References</dt>
+<dt>Relative Error</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 2010-12-22 05:22:56 EST (Wed, 22 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="id1283554"></a>
+<a name="id1401122"></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="id1283618"></a>
+<a name="id1401186"></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="id1283762"></a>
+<a name="id1401330"></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="id1283806"></a>
+<a name="id1401374"></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="id1283936"></a>
+<a name="id1402371"></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="id1284021"></a>
+<a name="id1402456"></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="id1284140"></a>
+<a name="id1402575"></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="id1284226"></a>
+<a name="id1402661"></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="id1284561"></a>
+<a name="id1402996"></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="id1284585"></a>
+<a name="id1403020"></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="id1284629"></a>
+<a name="id1403064"></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="id1285016"></a>
+<a name="id1403451"></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="id1285052"></a>
+<a name="id1403487"></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="id1285120"></a>
+<a name="id1403555"></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="id1285377"></a>
+<a name="id1403812"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1286443"></a>
+<a name="id1404141"></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="id1286701"></a>
+<a name="id1404399"></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="id1286893"></a>
+<a name="id1405302"></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="id1287051"></a>
+<a name="id1405460"></a>
 <a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.choosing_the_right_parameters">Choosing
 the Right Parameters</a>
 </h5>
@@ -535,16 +535,16 @@
 is exact, and so isn't used for the gamma function.
 
<a name="math_toolkit.backgrounders.lanczos.references"></a><h5>
-<a name="id1287589"></a>
+<a name="id1405998"></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">
+<div class="orderedlist"><ol type="1">
<li>
- Paul Godfrey, <a href="http://my.fit.edu/~gabdo/gamma.txt" target="_top">"A
+ <a name="godfrey"></a> Paul Godfrey, <a href="http://my.fit.edu/~gabdo/gamma.txt" target="_top">"A
 note on the computation of the convergent Lanczos complex Gamma approximation"</a>.
 </li>
<li>
- Glendon Ralph Pugh, <a href="http://bh0.physics.ubc.ca/People/matt/Doc/ThesesOthers/Phd/pugh.pdf" target="_top">"An
+ <a name="pugh"></a> Glendon Ralph Pugh, <a href="http://bh0.physics.ubc.ca/People/matt/Doc/ThesesOthers/Phd/pugh.pdf" target="_top">"An
 Analysis of the Lanczos Gamma Approximation"</a>, PhD Thesis
 November 2004.
 </li>

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 2010-12-22 05:22:56 EST (Wed, 22 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="id1288841"></a>
+<a name="id1406922"></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="id1288929"></a>
+<a name="id1407010"></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="id1288974"></a>
+<a name="id1407056"></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 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,8 +24,7 @@
</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
@@ -78,10 +77,8 @@
 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="id1286400"></a>
+<a name="zero_error"></a><a name="math_toolkit.backgrounders.relative_error.the_impossibility_of_zero_error"></a><h5>
+<a name="id1404098"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1287774"></a>
+<a name="id1406183"></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="id1287925"></a>
+<a name="id1406334"></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="id1288000"></a>
+<a name="id1406409"></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="id1288032"></a>
+<a name="id1406441"></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="id1288077"></a>
+<a name="id1406486"></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="id1288156"></a>
+<a name="id1406565"></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="id1288312"></a>
+<a name="id1406721"></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="id1288721"></a>
+<a name="id1406802"></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 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,186 +24,183 @@
</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
+<dt><a href="dist/dist_ref/dists/bernoulli_dist.html">Bernoulli
 Distribution</a></dt>
-<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
+<dt><a href="dist/dist_ref/dists/beta_dist.html">Beta
 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/binomial_dist.html">Binomial
 Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/extreme_dist.html"> Extreme
+<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
+ Distribution</a></dt>
+<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><a href="dist/dist_ref/dists/pareto.html"> Pareto
+<dt>Pareto Distribution</dt>
+<dt><a href="dist/dist_ref/dists/poisson_dist.html">Poisson
 Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/poisson_dist.html"> Poisson
+<dt><a href="dist/dist_ref/dists/rayleigh.html">Rayleigh
 Distribution</a></dt>
-<dt><a href="dist/dist_ref/dists/rayleigh.html"> Rayleigh
+<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/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
+<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 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,74 +24,73 @@
</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 Distribution</a></dt>
-<dt><a href="dist_ref/dists/beta_dist.html"> Beta
+<dt><a href="dist_ref/dists/bernoulli_dist.html">Bernoulli
 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/beta_dist.html">Beta
 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/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
 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><a href="dist_ref/dists/pareto.html"> Pareto
+<dt>Pareto Distribution</dt>
+<dt><a href="dist_ref/dists/poisson_dist.html">Poisson
 Distribution</a></dt>
-<dt><a href="dist_ref/dists/poisson_dist.html"> Poisson
+<dt><a href="dist_ref/dists/rayleigh.html">Rayleigh
 Distribution</a></dt>
-<dt><a href="dist_ref/dists/rayleigh.html"> Rayleigh
+<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/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
+<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 2010-12-22 05:22:56 EST (Wed, 22 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="id1058903"></a>
+<a name="id1177585"></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="id1059002"></a>
+<a name="id1177683"></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="id1059447"></a>
+<a name="id1178128"></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 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,67 +24,66 @@
</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 Distribution</a></dt>
-<dt><a href="dists/beta_dist.html"> Beta
+<dt><a href="dists/bernoulli_dist.html">Bernoulli
 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/beta_dist.html">Beta
 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/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
 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><a href="dists/pareto.html"> Pareto
+<dt>Pareto Distribution</dt>
+<dt><a href="dists/poisson_dist.html">Poisson
 Distribution</a></dt>
-<dt><a href="dists/poisson_dist.html"> Poisson
+<dt><a href="dists/rayleigh.html">Rayleigh
 Distribution</a></dt>
-<dt><a href="dists/rayleigh.html"> Rayleigh
+<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/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
+<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 2010-12-22 05:22:56 EST (Wed, 22 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="id997664"></a>
+<a name="id1116335"></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="id997742"></a>
+<a name="id1116413"></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="id997846"></a>
+<a name="id1116516"></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="id997867"></a>
+<a name="id1116537"></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="id998196"></a>
+<a name="id1116866"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id999084"></a>
+<a name="id1117955"></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="id999100"></a>
+<a name="id1117970"></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="id999215"></a>
+<a name="id1118085"></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="id999416"></a>
+<a name="id1118287"></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="id999866"></a>
+<a name="id1118737"></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="id999968"></a>
+<a name="id1118839"></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="id999994"></a>
+<a name="id1118864"></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="id1000040"></a>
+<a name="id1118911"></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="id1000085"></a>
+<a name="id1118955"></a>
 <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.implementation">Implementation</a>
 </h5>

@@ -500,8 +500,6 @@
 
 </td>
<td>
- 
- 
 </td>
</tr>
<tr>
@@ -596,7 +594,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.references"></a><h5>
-<a name="id1001367"></a>
+<a name="id1120097"></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 2010-12-22 05:22:56 EST (Wed, 22 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>


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

 <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>
@@ -136,43 +134,39 @@
</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="id1002317"></a>
+<a name="id1121045"></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="id1002335"></a>
+<a name="id1121063"></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);
@@ -189,7 +183,7 @@
 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="id1002453"></a>
+<a name="id1121181"></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;
@@ -205,7 +199,7 @@
 was constructed.
 
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.lower_bound_on_the_success_fraction"></a><h6>
-<a name="id1002533"></a>
+<a name="id1121261"></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>
@@ -311,7 +305,7 @@
 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="id1002987"></a>
+<a name="id1121715"></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>
@@ -389,7 +383,7 @@
</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="id1004480"></a>
+<a name="id1122030"></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>
@@ -431,7 +425,7 @@
 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="id1004682"></a>
+<a name="id1122232"></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>
@@ -479,7 +473,7 @@
 Worked Example.</a>
 
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.non_member_accessors"></a><h5>
-<a name="id1004892"></a>
+<a name="id1123694"></a>
 <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -628,7 +622,7 @@
</table></div>
</div>
 <a name="math_toolkit.dist.dist_ref.dists.binomial_dist.examples"></a><h5>
-<a name="id1005447"></a>
+<a name="id1124250"></a>
 <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.examples">Examples</a>
 </h5>

@@ -636,7 +630,7 @@
 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="id1005469"></a>
+<a name="id1124271"></a>
 <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.accuracy">Accuracy</a>
 </h5>

@@ -646,7 +640,7 @@
 please refer to these functions for information on accuracy.
 
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.implementation"></a><h5>
-<a name="id1005498"></a>
+<a name="id1124300"></a>
 <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.implementation">Implementation</a>
 </h5>

@@ -890,7 +884,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.references"></a><h5>
-<a name="id1006567"></a>
+<a name="id1125350"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1007086"></a>
+<a name="id1126018"></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="id1007233"></a>
+<a name="id1126166"></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="id1007376"></a>
+<a name="id1126309"></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="id1007410"></a>
+<a name="id1126342"></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="id1007636"></a>
+<a name="id1126569"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1008202"></a>
+<a name="id1127134"></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="id1008533"></a>
+<a name="id1127466"></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="id1009340"></a>
+<a name="id1127569"></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="id1009366"></a>
+<a name="id1127595"></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="id1009390"></a>
+<a name="id1127619"></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="id1009687"></a>
+<a name="id1127916"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1010121"></a>
+<a name="id1129223"></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="id1010222"></a>
+<a name="id1129323"></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="id1010321"></a>
+<a name="id1129423"></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="id1010369"></a>
+<a name="id1129471"></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="id1010636"></a>
+<a name="id1129737"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1011199"></a>
+<a name="id1130300"></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="id1011355"></a>
+<a name="id1130456"></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="id1011452"></a>
+<a name="id1130553"></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="id1012884"></a>
+<a name="id1130587"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1013647"></a>
+<a name="id1132580"></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="id1013800"></a>
+<a name="id1132733"></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="id1013900"></a>
+<a name="id1132833"></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="id1013922"></a>
+<a name="id1132854"></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="id1013948"></a>
+<a name="id1132881"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1015027"></a>
+<a name="id1133960"></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="id1015886"></a>
+<a name="id1134105"></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="id1015983"></a>
+<a name="id1134202"></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="id1016021"></a>
+<a name="id1134240"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1017204"></a>
+<a name="id1136206"></a>
 <a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.related_distributions">Related
 Distributions</a>
 </h5>
@@ -171,8 +171,6 @@
 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>
@@ -180,43 +178,40 @@
</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="id1017492"></a>
+<a name="id1136491"></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="id1017508"></a>
+<a name="id1136507"></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);
@@ -231,7 +226,7 @@
 1</code>.
 
<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.accessors"></a><h6>
-<a name="id1017587"></a>
+<a name="id1136586"></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)
@@ -258,7 +253,7 @@
 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="id1017695"></a>
+<a name="id1136694"></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>
@@ -313,7 +308,7 @@
 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="id1017926"></a>
+<a name="id1136925"></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>
@@ -368,7 +363,7 @@
 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="id1018359"></a>
+<a name="id1137153"></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>
@@ -420,7 +415,7 @@
 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="id1018598"></a>
+<a name="id1137391"></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>
@@ -468,7 +463,7 @@
 probability of observing more than k failures.
 
<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.non_member_accessors"></a><h5>
-<a name="id1018833"></a>
+<a name="id1138992"></a>
 <a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -616,7 +611,7 @@
</table></div>
</div>
 <a name="math_toolkit.dist.dist_ref.dists.geometric_dist.accuracy"></a><h5>
-<a name="id1019343"></a>
+<a name="id1139502"></a>
 <a class="link" href="geometric_dist.html#math_toolkit.dist.dist_ref.dists.geometric_dist.accuracy">Accuracy</a>
 </h5>

@@ -627,7 +622,7 @@
 for example to 10 decimal digits (from 16).
 
<a name="math_toolkit.dist.dist_ref.dists.geometric_dist.implementation"></a><h5>
-<a name="id1019375"></a>
+<a name="id1139535"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1022757"></a>
+<a name="id1140522"></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="id1022936"></a>
+<a name="id1140701"></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="id1023086"></a>
+<a name="id1140851"></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="id1023320"></a>
+<a name="id1142315"></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="id1023344"></a>
+<a name="id1142339"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1024371"></a>
+<a name="id1143366"></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="id1024543"></a>
+<a name="id1143537"></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="id1024647"></a>
+<a name="id1143642"></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="id1024688"></a>
+<a name="id1143683"></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="id1025889"></a>
+<a name="id1144011"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1026470"></a>
+<a name="id1146020"></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="id1026607"></a>
+<a name="id1146157"></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="id1026713"></a>
+<a name="id1146264"></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="id1026752"></a>
+<a name="id1146302"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1027685"></a>
+<a name="id1147236"></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="id1027826"></a>
+<a name="id1147376"></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="id1027933"></a>
+<a name="id1147483"></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="id1027955"></a>
+<a name="id1147506"></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="id1028580"></a>
+<a name="id1147801"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1029166"></a>
+<a name="id1148512"></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="id1029328"></a>
+<a name="id1148674"></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="id1029425"></a>
+<a name="id1148771"></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="id1029444"></a>
+<a name="id1148790"></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="id1029766"></a>
+<a name="id1149112"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1030256"></a>
+<a name="id1149601"></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="id1030421"></a>
+<a name="id1149767"></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="id1031685"></a>
+<a name="id1149917"></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="id1031740"></a>
+<a name="id1149972"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1032490"></a>
+<a name="id1151838"></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="id1032650"></a>
+<a name="id1151997"></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="id1032749"></a>
+<a name="id1152097"></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="id1032777"></a>
+<a name="id1152125"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1038037"></a>
+<a name="id1157525"></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="id1038223"></a>
+<a name="id1157711"></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="id1038332"></a>
+<a name="id1157820"></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="id1038574"></a>
+<a name="id1158063"></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="id1038598"></a>
+<a name="id1158087"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1040748"></a>
+<a name="id1160919"></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="id1041649"></a>
+<a name="id1161820"></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="id1041749"></a>
+<a name="id1161920"></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="id1041777"></a>
+<a name="id1161948"></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="id1042037"></a>
+<a name="id1162208"></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="id1042056"></a>
+<a name="id1162227"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1044356"></a>
+<a name="id1163555"></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="id1044544"></a>
+<a name="id1163743"></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="id1044644"></a>
+<a name="id1163843"></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="id1044668"></a>
+<a name="id1163867"></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="id1044692"></a>
+<a name="id1163891"></a>
 <a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.implementation">Implementation</a>
 </h5>

@@ -234,8 +234,6 @@
 
 y = x * v1 / v2
 
- 
- 
 </td>
</tr>
<tr>
@@ -258,8 +256,6 @@
 
 y = x * v1 / v2
 
- 
- 
 </td>
</tr>
<tr>
@@ -290,8 +286,6 @@
 
 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 2010-12-22 05:22:56 EST (Wed, 22 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="id1045587"></a>
+<a name="id1164775"></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="id1045726"></a>
+<a name="id1164914"></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="id1045826"></a>
+<a name="id1165014"></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="id1046037"></a>
+<a name="id1165214"></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="id1046057"></a>
+<a name="id1165233"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1034014"></a>
+<a name="id1153272"></a>
 <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.related_distributions">Related
 Distributions</a>
 </h5>
@@ -160,8 +160,6 @@

 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>
@@ -169,43 +167,40 @@
</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="id1034124"></a>
+<a name="id1153380"></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="id1034137"></a>
+<a name="id1153393"></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);
@@ -221,7 +216,7 @@
 <= 1</code>.
 
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accessors"></a><h6>
-<a name="id1034247"></a>
+<a name="id1153502"></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)
@@ -242,7 +237,7 @@
 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="id1034340"></a>
+<a name="id1153596"></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>
@@ -303,7 +298,7 @@
 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="id1034608"></a>
+<a name="id1154032"></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>
@@ -363,7 +358,7 @@
 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="id1034872"></a>
+<a name="id1154296"></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>
@@ -414,7 +409,7 @@
 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="id1035096"></a>
+<a name="id1154521"></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>
@@ -462,7 +457,7 @@
 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="id1035328"></a>
+<a name="id1154752"></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>
@@ -611,7 +606,7 @@
</table></div>
</div>
 <a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accuracy"></a><h5>
-<a name="id1035841"></a>
+<a name="id1155266"></a>
 <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accuracy">Accuracy</a>
 </h5>

@@ -621,7 +616,7 @@
 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="id1035868"></a>
+<a name="id1155292"></a>
 <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.implementation">Implementation</a>
 </h5>

@@ -832,8 +827,6 @@
 
 </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 2010-12-22 05:22:56 EST (Wed, 22 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="id1046771"></a>
+<a name="id1166177"></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="id1046966"></a>
+<a name="id1166373"></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="id1047063"></a>
+<a name="id1166470"></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="id1047089"></a>
+<a name="id1166495"></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 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,8 +24,7 @@
</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>


@@ -87,12 +86,12 @@
 <img src="../../../../../graphs/pareto_pdf2.png" align="middle">
 
<a name="math_toolkit.dist.dist_ref.dists.pareto.related_distributions"></a><h5>
-<a name="id1047872"></a>
+<a name="id1167279"></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="id1047890"></a>
+<a name="id1167297"></a>
 <a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.member_functions">Member
 Functions</a>
 </h5>
@@ -118,7 +117,7 @@
 Returns the shape parameter of this distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.pareto.non_member_accessors"></a><h5>
-<a name="id1048058"></a>
+<a name="id1167465"></a>
 <a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -138,7 +137,7 @@
 The supported domain of the random variable is [scale, ∞].
 
<a name="math_toolkit.dist.dist_ref.dists.pareto.accuracy"></a><h5>
-<a name="id1048158"></a>
+<a name="id1167565"></a>
 <a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.accuracy">Accuracy</a>
 </h5>

@@ -151,7 +150,7 @@
 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="id1049704"></a>
+<a name="id1167602"></a>
 <a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.implementation">Implementation</a>
 </h5>

@@ -319,7 +318,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.pareto.references"></a><h5>
-<a name="id1050011"></a>
+<a name="id1167909"></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 2010-12-22 05:22:56 EST (Wed, 22 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>

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

 <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>
@@ -91,38 +89,34 @@
</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="id1050544"></a>
+<a name="id1170155"></a>
 <a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.member_functions">Member
 Functions</a>
 </h5>
@@ -137,7 +131,7 @@
 Returns the mean of this distribution.
 
<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.non_member_accessors"></a><h5>
-<a name="id1050633"></a>
+<a name="id1170244"></a>
 <a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.non_member_accessors">Non-member
 Accessors</a>
 </h5>
@@ -157,7 +151,7 @@
 The domain of the random variable is [0, ∞].
 
<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.accuracy"></a><h5>
-<a name="id1050730"></a>
+<a name="id1170341"></a>
 <a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.accuracy">Accuracy</a>
 </h5>

@@ -171,7 +165,7 @@
 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="id1050759"></a>
+<a name="id1170370"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1051480"></a>
+<a name="id1171091"></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="id1051532"></a>
+<a name="id1171142"></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="id1051635"></a>
+<a name="id1171246"></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="id1051735"></a>
+<a name="id1171345"></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="id1051768"></a>
+<a name="id1171379"></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="id1052395"></a>
+<a name="id1171715"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1052976"></a>
+<a name="id1172855"></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="id1053266"></a>
+<a name="id1173145"></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="id1053366"></a>
+<a name="id1173245"></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="id1053392"></a>
+<a name="id1173271"></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="id1053423"></a>
+<a name="id1173302"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1055682"></a>
+<a name="id1174332"></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="id1055900"></a>
+<a name="id1174550"></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="id1056000"></a>
+<a name="id1174650"></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="id1056022"></a>
+<a name="id1174672"></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="id1056362"></a>
+<a name="id1175030"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1057042"></a>
+<a name="id1175709"></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="id1057207"></a>
+<a name="id1175875"></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="id1057312"></a>
+<a name="id1175979"></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="id1057331"></a>
+<a name="id1175998"></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="id1057609"></a>
+<a name="id1176277"></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 2010-12-22 05:22:56 EST (Wed, 22 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="id1058169"></a>
+<a name="id1176836"></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="id1058207"></a>
+<a name="id1176874"></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="id1058363"></a>
+<a name="id1177045"></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="id1058461"></a>
+<a name="id1177142"></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="id1058504"></a>
+<a name="id1177185"></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="id1058836"></a>
+<a name="id1177517"></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 2010-12-22 05:22:56 EST (Wed, 22 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
@@ -36,10 +36,9 @@
 <a class="link" href="nmp.html#function_index">function index</a> to go straight to
 the function you want if you already know its name.
 
-<a name="function_index"></a><a name="math_toolkit.dist.dist_ref.nmp.function_index"></a><h5>
-<a name="id990180"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.function_index">Function
- Index</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__function_index____function_index"></a><h5>
+<a name="id1108768"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__function_index____function_index"><a name="function_index"></a> Function Index</a>
 </h5>
<div class="itemizedlist"><ul type="disc">
<li>
@@ -94,10 +93,9 @@
 <a class="link" href="nmp.html#math.dist.variance">variance</a>.
 </li>
</ul></div>
-<a name="concept_index"></a><a name="math_toolkit.dist.dist_ref.nmp.conceptual_index"></a><h5>
-<a name="id990405"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.conceptual_index">Conceptual
- Index</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__concept_index____conceptual_index"></a><h5>
+<a name="id1108992"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__concept_index____conceptual_index"><a name="concept_index"></a> Conceptual Index</a>
 </h5>
<div class="itemizedlist"><ul type="disc">
<li>
@@ -181,10 +179,9 @@
 <a class="link" href="nmp.html#math.dist.variance">variance</a>.
 </li>
</ul></div>
-<a name="math.dist.cdf"></a><a name="math_toolkit.dist.dist_ref.nmp.cumulative_distribution_function"></a><h5>
-<a name="id990776"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.cumulative_distribution_function">Cumulative
- Distribution Function</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_cdf____cumulative_distribution_function"></a><h5>
+<a name="id1109324"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_cdf____cumulative_distribution_function"><a name="math.dist.cdf"></a> Cumulative Distribution Function</a>
 </h5>
<pre class="programlisting">template <class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
RealType cdf(const Distribution-Type<RealType, <a class="link" href="../../policy.html" title="Policies">Policy</a>>& dist, const RealType& x);
@@ -205,10 +202,9 @@

 <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="id990947"></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>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_ccdf____complement_of_the_cumulative_distribution_function"></a><h5>
+<a name="id1109491"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_ccdf____complement_of_the_cumulative_distribution_function"><a name="math.dist.ccdf"></a> Complement of the Cumulative Distribution Function</a>
 </h5>
<pre class="programlisting">template <class Distribution, class RealType>
RealType cdf(const Unspecified-Complement-Type<Distribution, RealType>& comp);
@@ -246,9 +242,9 @@
 See <a class="link" href="../stat_tut/overview/complements.html#why_complements">why complements?</a> for why the
 complement is useful and when it should be used.
 
-<a name="math.dist.hazard"></a><a name="math_toolkit.dist.dist_ref.nmp.hazard_function"></a><h5>
-<a name="id991236"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.hazard_function">Hazard Function</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_hazard____hazard_function"></a><h5>
+<a name="id1109873"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_hazard____hazard_function"><a name="math.dist.hazard"></a> Hazard Function</a>
 </h5>
<pre class="programlisting">template <class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
RealType hazard(const Distribution-Type<RealType, <a class="link" href="../../policy.html" title="Policies">Policy</a>>& dist, const RealType& x);
@@ -274,10 +270,9 @@
 rather than the hazard function.
 </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="id991418"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.cumulative_hazard_function">Cumulative
- Hazard Function</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_chf____cumulative_hazard_function"></a><h5>
+<a name="id1110052"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_chf____cumulative_hazard_function"><a name="math.dist.chf"></a> Cumulative Hazard Function</a>
 </h5>
<pre class="programlisting">template <class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
RealType chf(const Distribution-Type<RealType, <a class="link" href="../../policy.html" title="Policies">Policy</a>>& dist, const RealType& x);
@@ -302,9 +297,9 @@
 Some authors refer to this as simply the "Hazard Function".
 </td></tr>
</table></div>
-<a name="math.dist.mean"></a><a name="math_toolkit.dist.dist_ref.nmp.mean"></a><h5>
-<a name="id991601"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.mean">mean</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_mean____mean"></a><h5>
+<a name="id1110230"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_mean____mean"><a name="math.dist.mean"></a> mean</a>
 </h5>
<pre class="programlisting">template<class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
RealType mean(const Distribution-Type<RealType, <a class="link" href="../../policy.html" title="Policies">Policy</a>>& dist);
@@ -317,9 +312,9 @@
 if the distribution does not have a defined mean (for example the Cauchy
 distribution).
 
-<a name="math.dist.median"></a><a name="math_toolkit.dist.dist_ref.nmp.median"></a><h5>
-<a name="id991718"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.median">median</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_median____median"></a><h5>
+<a name="id1110347"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_median____median"><a name="math.dist.median"></a> median</a>
 </h5>
<pre class="programlisting">template<class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
RealType median(const Distribution-Type<RealType, <a class="link" href="../../policy.html" title="Policies">Policy</a>>& dist);
@@ -327,9 +322,9 @@

 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="id991827"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.mode">mode</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_mode____mode"></a><h5>
+<a name="id1110455"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_mode____mode"><a name="math.dist.mode"></a> mode</a>
 </h5>
<pre class="programlisting">template<class RealType, <a class="link" href="../../policy.html" title="Policies">Policy</a>>
RealType mode(const Distribution-Type<RealType, <a class="link" href="../../policy.html" title="Policies">Policy</a>>& dist);
@@ -341,10 +336,9 @@
 This function may return a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
 if the distribution does not have a defined mode.
 
-<a name="math.dist.pdf"></a><a name="math_toolkit.dist.dist_ref.nmp.probability_density_function"></a><h5>
-<a name="id991943"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.probability_density_function">Probability
- Density Function</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_pdf____probability_density_function"></a><h5>
+<a name="id1110566"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_pdf____probability_density_function"><a name="math.dist.pdf"></a> Probability Density Function</a>
 </h5>
<pre class="programlisting">template <class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
RealType pdf(const Distribution-Type<RealType, <a class="link" href="../../policy.html" title="Policies">Policy</a>>& dist, const RealType& x);
@@ -370,9 +364,9 @@

 <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="id992112"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.range">Range</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_range____range"></a><h5>
+<a name="id1110732"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_range____range"><a name="math.dist.range"></a> Range</a>
 </h5>
<pre class="programlisting">template<class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
std::pair<RealType, RealType> range(const Distribution-Type<RealType, <a class="link" href="../../policy.html" title="Policies">Policy</a>>& dist);
@@ -380,9 +374,9 @@

 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="id992247"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.quantile">Quantile</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_quantile____quantile"></a><h5>
+<a name="id1110866"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_quantile____quantile"><a name="math.dist.quantile"></a> Quantile</a>
 </h5>
<pre class="programlisting">template <class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
RealType quantile(const Distribution-Type<RealType, <a class="link" href="../../policy.html" title="Policies">Policy</a>>& dist, const RealType& p);
@@ -410,13 +404,12 @@

 <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="id992474"></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>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_quantile_c____quantile_from_the_complement_of_the_probability_"></a><h5>
+<a name="id1111092"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_quantile_c____quantile_from_the_complement_of_the_probability_"><a name="math.dist.quantile_c"></a> Quantile from the complement of the probability.</a>
 </h5>

- <a class="link" href="../stat_tut/overview.html#complements">complements</a>
+ <a class="link" href="../stat_tut/overview/complements.html#complements">complements</a>
 
<pre class="programlisting">template <class Distribution, class RealType>
RealType quantile(const Unspecified-Complement-Type<Distribution, RealType>& comp);
@@ -456,10 +449,9 @@

 <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="id992815"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.standard_deviation">Standard
- Deviation</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_sd____standard_deviation"></a><h5>
+<a name="id1111430"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_sd____standard_deviation"><a name="math.dist.sd"></a> Standard Deviation</a>
 </h5>
<pre class="programlisting">template <class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
RealType standard_deviation(const Distribution-Type<RealType, <a class="link" href="../../policy.html" title="Policies">Policy</a>>& dist);
@@ -471,9 +463,9 @@
 This function may return a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
 if the distribution does not have a defined standard deviation.
 
-<a name="math.dist.support"></a><a name="math_toolkit.dist.dist_ref.nmp.support"></a><h5>
-<a name="id996212"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.support">support</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_support____support"></a><h5>
+<a name="id1111549"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_support____support"><a name="math.dist.support"></a> support</a>
 </h5>
<pre class="programlisting">template<class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
std::pair<RealType, RealType> support(const Distribution-Type<RealType, <a class="link" href="../../policy.html" title="Policies">Policy</a>>& dist);
@@ -488,9 +480,9 @@
 that has the cdf going from zero to unity. Outside are uninteresting zones
 where the pdf is zero, and the cdf zero or unity.
 
-<a name="math.dist.variance"></a><a name="math_toolkit.dist.dist_ref.nmp.variance"></a><h5>
-<a name="id996356"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.variance">Variance</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_variance____variance"></a><h5>
+<a name="id1111692"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_variance____variance"><a name="math.dist.variance"></a> Variance</a>
 </h5>
<pre class="programlisting">template <class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
RealType variance(const Distribution-Type<RealType, <a class="link" href="../../policy.html" title="Policies">Policy</a>>& dist);
@@ -502,9 +494,9 @@
 This function may return a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
 if the distribution does not have a defined variance.
 
-<a name="math.dist.skewness"></a><a name="math_toolkit.dist.dist_ref.nmp.skewness"></a><h5>
-<a name="id996475"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.skewness">Skewness</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_skewness____skewness"></a><h5>
+<a name="id1111810"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_skewness____skewness"><a name="math.dist.skewness"></a> Skewness</a>
 </h5>
<pre class="programlisting">template <class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
RealType skewness(const Distribution-Type<RealType, <a class="link" href="../../policy.html" title="Policies">Policy</a>>& dist);
@@ -516,9 +508,9 @@
 This function may return a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
 if the distribution does not have a defined skewness.
 
-<a name="math.dist.kurtosis"></a><a name="math_toolkit.dist.dist_ref.nmp.kurtosis"></a><h5>
-<a name="id996594"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.kurtosis">Kurtosis</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_kurtosis____kurtosis"></a><h5>
+<a name="id1111927"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_kurtosis____kurtosis"><a name="math.dist.kurtosis"></a> Kurtosis</a>
 </h5>
<pre class="programlisting">template <class RealType, class <a class="link" href="../../policy.html" title="Policies">Policy</a>>
RealType kurtosis(const Distribution-Type<RealType, <a class="link" href="../../policy.html" title="Policies">Policy</a>>& dist);
@@ -558,10 +550,9 @@

 '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="id996802"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.kurtosis_excess">Kurtosis
- excess</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_kurtosis_excess____kurtosis_excess"></a><h5>
+<a name="id1115484"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__math_dist_kurtosis_excess____kurtosis_excess"><a name="math.dist.kurtosis_excess"></a> Kurtosis excess</a>
 </h5>
<pre class="programlisting">template <class RealType, <a class="link" href="../../policy.html" title="Policies">Policy</a>>
RealType kurtosis_excess(const Distribution-Type<RealType, <a class="link" href="../../policy.html" title="Policies">Policy</a>>& dist);
@@ -593,9 +584,9 @@

 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="id996988"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.p_and_q">P and Q</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__cdfpq____p_and_q"></a><h5>
+<a name="id1115671"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__cdfpq____p_and_q"><a name="cdfPQ"></a> P and Q</a>
 </h5>

 The terms P and Q are sometimes used to refer to the <a class="link" href="nmp.html#math.dist.cdf">Cumulative
@@ -603,36 +594,32 @@
 respectively. Lowercase p and q are sometimes used to refer to the values
 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="id997018"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.percent_point_function_or_percentile">Percent
- Point Function or Percentile</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__percent____percent_point_function_or_percentile"></a><h5>
+<a name="id1115702"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__percent____percent_point_function_or_percentile"><a name="percent"></a> Percent Point Function or Percentile</a>
 </h5>

 The percent point function, also known as the percentile, is the same as
 the <a class="link" href="nmp.html#math.dist.quantile">Quantile</a>.
 
-<a name="cdf_inv"></a><a name="math_toolkit.dist.dist_ref.nmp.inverse_cdf_function_"></a><h5>
-<a name="id997043"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.inverse_cdf_function_">Inverse
- CDF Function.</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__cdf_inv____inverse_cdf_function_"></a><h5>
+<a name="id1115726"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__cdf_inv____inverse_cdf_function_"><a name="cdf_inv"></a> Inverse CDF Function.</a>
 </h5>

 The inverse of the cumulative distribution function, is the same as the
 <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="id997070"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.inverse_survival_function_">Inverse
- Survival Function.</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__survival_inv____inverse_survival_function_"></a><h5>
+<a name="id1115750"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__survival_inv____inverse_survival_function_"><a name="survival_inv"></a> Inverse Survival Function.</a>
 </h5>

 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="id997100"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.probability_mass_function">Probability
- Mass Function</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__pmf____probability_mass_function"></a><h5>
+<a name="id1115774"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__pmf____probability_mass_function"><a name="pmf"></a> Probability Mass Function</a>
 </h5>

 The Probability Mass Function is the same as the <a class="link" href="nmp.html#math.dist.pdf">Probability
@@ -643,20 +630,18 @@
 the term <a class="link" href="nmp.html#math.dist.pdf">Probability Density Function</a>
 applies to continuous distributions.
 
-<a name="lower_critical"></a><a name="math_toolkit.dist.dist_ref.nmp.lower_critical_value_"></a><h5>
-<a name="id997139"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.lower_critical_value_">Lower
- Critical Value.</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__lower_critical____lower_critical_value_"></a><h5>
+<a name="id1115809"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__lower_critical____lower_critical_value_"><a name="lower_critical"></a> Lower Critical Value.</a>
 </h5>

 The lower critical value calculates the value of the random variable given
 the area under the left tail of the distribution. It is equivalent to calculating
 the <a class="link" href="nmp.html#math.dist.quantile">Quantile</a>.
 
-<a name="upper_critical"></a><a name="math_toolkit.dist.dist_ref.nmp.upper_critical_value_"></a><h5>
-<a name="id997164"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.upper_critical_value_">Upper
- Critical Value.</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__upper_critical____upper_critical_value_"></a><h5>
+<a name="id1115833"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__upper_critical____upper_critical_value_"><a name="upper_critical"></a> Upper Critical Value.</a>
 </h5>

 The upper critical value calculates the value of the random variable given
@@ -664,10 +649,9 @@
 calculating the <a class="link" href="nmp.html#math.dist.quantile_c">quantile from the
 complement of the probability</a>.
 
-<a name="survival"></a><a name="math_toolkit.dist.dist_ref.nmp.survival_function"></a><h5>
-<a name="id997190"></a>
- <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.survival_function">Survival
- Function</a>
+<a name="math_toolkit.dist.dist_ref.nmp._anchor_id__survival____survival_function"></a><h5>
+<a name="id1115858"></a>
+ <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp._anchor_id__survival____survival_function"><a name="survival"></a> Survival Function</a>
 </h5>

 Refer to the <a class="link" href="nmp.html#math.dist.ccdf">Complement of the Cumulative

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/future.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/future.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/future.html 2010-12-22 05:22:56 EST (Wed, 22 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="id1061708"></a>
+<a name="id1178614"></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="id1061873"></a>
+<a name="id1178779"></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="id1062094"></a>
+<a name="id1178999"></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="id1062256"></a>
+<a name="id1185887"></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 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,112 +24,110 @@
</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 2010-12-22 05:22:56 EST (Wed, 22 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 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,23 +24,21 @@
</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>
- 
</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 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,10 +24,10 @@
</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>
-
+<a name="complements"></a>
 Often you don't want the value of the CDF, but its complement, which
 is to say <code class="computeroutput">1-p</code> rather than <code class="computeroutput">p</code>.
 It is tempting to calculate the CDF and subtract it from <code class="computeroutput">1</code>, but if <code class="computeroutput">p</code>
@@ -70,8 +70,6 @@
</tr>
<tr><td align="left" valign="top">

- 
-
 Critical values are just quantiles
 

@@ -105,8 +103,6 @@
 
</td></tr>
</table></div>
-<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>
@@ -114,9 +110,8 @@
</tr>
<tr><td align="left" valign="top">

- 
-
- Why bother with complements anyway?
+ <a name="why_complements"></a> Why bother with
+ complements anyway?
 

 It's very tempting to dispense with complements, and simply subtract
@@ -186,8 +181,6 @@
 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 2010-12-22 05:22:56 EST (Wed, 22 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>

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

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

- 
-
 Random Variates and Distribution Parameters
 

@@ -194,8 +190,6 @@
</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 2010-12-22 05:22:56 EST (Wed, 22 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 2010-12-22 05:22:56 EST (Wed, 22 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 2010-12-22 05:22:56 EST (Wed, 22 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 2010-12-22 05:22:56 EST (Wed, 22 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 2010-12-22 05:22:56 EST (Wed, 22 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 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,96 +24,90 @@
</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 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,19 +24,18 @@
</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 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,9 +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_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 2010-12-22 05:22:56 EST (Wed, 22 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 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,48 +24,36 @@
</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.
- 
-
- 
-
- 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).
- 
-
- 
+ 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.
+ 

- (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.
+ 

- 
+ 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).
+ 

- First we need some includes and using statements to be able to use
- the binomial distribution, some std input and output, and get started:
- 
+ (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;
@@ -81,23 +69,17 @@
 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;
@@ -105,16 +87,12 @@

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;
@@ -130,141 +108,104 @@
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;
@@ -288,58 +229,42 @@
 << 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
@@ -386,8 +311,6 @@
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 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,33 +24,27 @@
</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;
@@ -66,50 +60,38 @@

</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;
@@ -120,10 +102,7 @@
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
@@ -131,20 +110,13 @@
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++)
@@ -154,10 +126,7 @@
}
cout << endl;</pre>

- 
-
-
-
+ 
<pre class="programlisting">Guessed Probability
 0 0.0100226
 1 0.0534538
@@ -178,152 +147,101 @@
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 "
@@ -332,21 +250,14 @@

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++)
@@ -356,10 +267,7 @@
}
cout << endl;</pre>

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

- 
-
-
+

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

- 
-
-
-
+ 
<pre class="programlisting">At least (>)
Guessed OK Probability
 0 0.9899774042
@@ -417,21 +320,15 @@
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.
@@ -445,40 +342,26 @@
 << 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 "
@@ -490,32 +373,22 @@
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="id1055469"></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>

- <a name="math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.using_binomial_distribution_moments"></a>
- 
-<h5>
-<a name="id936646"></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.
- 
-
- 
+ 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;
@@ -525,33 +398,23 @@
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="id1055958"></a>
+ <a class="link" href="binomial_quiz_example.html#math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.quantiles">Quantiles</a>
+ </h5>

- <a name="math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.quantiles"></a>
- 
-<h5>
-<a name="id937081"></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:
- 
-
- 
+ 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
@@ -569,16 +432,11 @@
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
@@ -587,111 +445,74 @@
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.
+ 

- 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
- 
+ 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
+ 
<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.
+ 

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



-<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
@@ -709,10 +530,7 @@
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
@@ -723,8 +541,6 @@
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 2010-12-22 05:22:56 EST (Wed, 22 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 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,17 +24,16 @@
</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 2010-12-22 05:22:56 EST (Wed, 22 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="id921412"></a>
+<a name="id1040390"></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 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,9 +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_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 2010-12-22 05:22:56 EST (Wed, 22 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 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,34 +24,28 @@
</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.
@@ -61,240 +55,167 @@
#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);
@@ -317,65 +238,40 @@
// 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="id910528"></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="id1029538"></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;

@@ -386,13 +282,9 @@
 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 2010-12-22 05:22:56 EST (Wed, 22 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>

@@ -43,68 +43,43 @@
 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:
- 
+ 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>

- 
-
- is a certain sign that it will not have the desired
- effect.
- 
-
- 
-
- We'll begin our sample program with the needed includes:
- 
+ 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>
@@ -121,18 +96,14 @@
#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()
{
@@ -168,16 +139,11 @@
 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

@@ -186,52 +152,30 @@
 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 2010-12-22 05:22:56 EST (Wed, 22 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 2010-12-22 05:22:56 EST (Wed, 22 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 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,19 +24,15 @@
</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.
@@ -58,34 +54,26 @@

</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
@@ -99,66 +87,44 @@
 << ", 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
@@ -167,53 +133,37 @@
 << " 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="id1096497"></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).
+ 

- <a name="math_toolkit.dist.stat_tut.weg.find_eg.find_location_eg.controlling_error_handling_from_find_location"></a>
- 
-<h5>
-<a name="id976741"></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:
- 
-
- 
+ 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.
@@ -225,19 +175,15 @@
// 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/complements.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.
@@ -250,11 +196,11 @@
 << "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
@@ -264,8 +210,6 @@
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 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,19 +24,15 @@
</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.
@@ -59,108 +55,78 @@
 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="id983969"></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="id1102559"></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.
+ 

- We start by constructing a normal distribution with the given parameters:
- 
+ "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);
@@ -169,17 +135,13 @@
 << " 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;
@@ -193,94 +155,69 @@
 << " 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="id1103740"></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.
+ 

- <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="id985182"></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.
- 
+ 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.
+ 

-
+

<pre class="programlisting">cauchy cpacks(mean, standard_deviation);
cout << "Cauchy Setting the packer to " << mean << " will mean that "
@@ -288,39 +225,29 @@
 << " 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 "
@@ -328,17 +255,13 @@
 << " 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)
@@ -346,114 +269,81 @@
 << "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.
- 
-
- 
-
- 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.
- 
-
- 
-
- 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.
- 
+ 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.
+ 

- <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="id985830"></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>
+ 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.
+ 

- 
+ 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.
- 
+ 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.
+ 

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

- This might cost more, but would reduce the amount we have to 'give
- away' in order to meet the specification.
- 
+ 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="id1104418"></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.
+ 

- 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
- 
+ 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)
@@ -465,20 +355,15 @@
 << " 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)
@@ -490,46 +375,34 @@
 << " 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.
- 
-
- 
-
- 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).
- 
+ 

- 
+ 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>.
+ 

- 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.
+ 

- 
+ 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).
+ 

- Rearranging, we can directly calculate the required standard deviation:
- 
+ 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;
@@ -540,17 +413,13 @@
 << 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
@@ -558,108 +427,75 @@
 << " 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/complements.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
@@ -667,45 +503,31 @@
 << " 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 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.
- 
+ 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 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,20 +24,16 @@
</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.
@@ -54,35 +50,27 @@
 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
@@ -96,70 +84,46 @@
 << ", 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
@@ -168,53 +132,37 @@
 << " 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="id1100350"></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).
+ 

- <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="id981282"></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:
- 
-
- 
+ 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.
@@ -227,20 +175,16 @@
// 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/complements.html#complements">complements</a> version.
+ 

-
+

<pre class="programlisting">z = -2.;
double q = 0.999; // = 1 - p; // complement of 0.001.
@@ -252,31 +196,24 @@
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
@@ -286,8 +223,6 @@
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/geometric_eg.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/geometric_eg.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/geometric_eg.html 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,50 +24,39 @@
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
-<a name="math_toolkit.dist.stat_tut.weg.geometric_eg"></a><a class="link" href="geometric_eg.html" title="Geometric Distribution Examples"> Geometric
+<a name="math_toolkit.dist.stat_tut.weg.geometric_eg"></a><a class="link" href="geometric_eg.html" title="Geometric Distribution Examples">Geometric
 Distribution Examples</a>
</h5></div></div></div>

- 
-
- For this example, we will opt to #define two macros to control the
- error and discrete handling policies. For this simple example, we want
- to avoid throwing an exception (the default policy) and just return
- infinity. We want to treat the distribution as if it was continuous,
- so we choose a discrete_quantile policy of real, rather than the default
- policy integer_round_outwards.
- 
-
- 
+ For this example, we will opt to #define two macros to control the error
+ and discrete handling policies. For this simple example, we want to avoid
+ throwing an exception (the default policy) and just return infinity.
+ We want to treat the distribution as if it was continuous, so we choose
+ a discrete_quantile policy of real, rather than the default policy integer_round_outwards.
+ 

-
+

<pre class="programlisting">#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
#define BOOST_MATH_DISCRETE_QUANTILE_POLICY real</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">
- It is vital to #include distributions etc after
- the above #defines
- </td></tr>
+ It is vital to #include distributions etc after
+ the above #defines
+ </td></tr>
</table></div>

- 
-
- After that we need some includes to provide easy access to the negative
- binomial distribution, and we need some std library iostream, of course.
- 
-
- 
+ After that we need some includes to provide easy access to the negative
+ binomial distribution, and we need some std library iostream, of course.
+ 

-
+

<pre class="programlisting">#include <boost/math/distributions/geometric.hpp>
 // for geometric_distribution
@@ -95,240 +84,173 @@
 using std::numeric_limits;
</pre>

- 
-
- 
-
- It is always sensible to use try and catch blocks because defaults
- policies are to throw an exception if anything goes wrong.
- 
-
- 
-
- Simple try'n'catch blocks (see below) will ensure that you get a helpful
- error message instead of an abrupt (and silent) program abort.
- 
-
- <a name="math_toolkit.dist.stat_tut.weg.geometric_eg.throwing_a_dice"></a>
- 
-<h6>
-<a name="id944551"></a>
- <a class="link" href="geometric_eg.html#math_toolkit.dist.stat_tut.weg.geometric_eg.throwing_a_dice">Throwing
- a dice</a>
- </h6>
-
- 
-
- The Geometric distribution describes the probability (p)
- of a number of failures to get the first success in k
- Bernoulli trials. (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).
- 
+ 

- 
+ It is always sensible to use try and catch blocks because defaults policies
+ are to throw an exception if anything goes wrong.
+ 

- Suppose an 'fair' 6-face dice is thrown repeatedly:
- 
+ Simple try'n'catch blocks (see below) will ensure that you get a helpful
+ error message instead of an abrupt (and silent) program abort.
+ 
+<a name="math_toolkit.dist.stat_tut.weg.geometric_eg.throwing_a_dice"></a><h6>
+<a name="id1063432"></a>
+ <a class="link" href="geometric_eg.html#math_toolkit.dist.stat_tut.weg.geometric_eg.throwing_a_dice">Throwing
+ a dice</a>
+ </h6>
+
+ The Geometric distribution describes the probability (p)
+ of a number of failures to get the first success in k
+ Bernoulli trials. (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).
+ 

- 
+ Suppose an 'fair' 6-face dice is thrown repeatedly:
+ 

-
+

<pre class="programlisting">double success_fraction = 1./6; // success_fraction (p) = 0.1666
// (so failure_fraction is 1 - success_fraction = 5./6 = 1- 0.1666 = 0.8333)</pre>

- 
-
- 
-
- If the dice is thrown repeatedly until the first
- time a three appears. The probablility distribution
- of the number of times it is thrown not
- getting a three (not-a-threes
- number of failures to get a three) is a geometric
- distribution with the success_fraction = 1/6 = 0.1666 ̇.
- 
-
- 
+ 

- We therefore start by constructing a geometric distribution with the
- one parameter success_fraction, the probability of success.
- 
+ If the dice is thrown repeatedly until the first
+ time a three appears. The probablility distribution
+ of the number of times it is thrown not
+ getting a three (not-a-threes
+ number of failures to get a three) is a geometric
+ distribution with the success_fraction = 1/6 = 0.1666 ̇.
+ 

- 
+ We therefore start by constructing a geometric distribution with the
+ one parameter success_fraction, the probability of success.
+ 

-
+

<pre class="programlisting">geometric g6(success_fraction); // type double by default.</pre>

- 
-
- 
-
- To confirm, we can echo the success_fraction parameter of the distribution.
- 
+ 

- 
+ To confirm, we can echo the success_fraction parameter of the distribution.
+ 

-
+

<pre class="programlisting">cout << "success fraction of a six-sided dice is " << g6.success_fraction() << endl;</pre>

- 
-
- 
-
- So the probability of getting a three at the first throw (zero failures)
- is
- 
+ 

- 
+ So the probability of getting a three at the first throw (zero failures)
+ is
+ 

-
+

<pre class="programlisting">cout << pdf(g6, 0) << endl; // 0.1667
cout << cdf(g6, 0) << endl; // 0.1667</pre>

- 
-
- 
-
- Note that the cdf and pdf are identical because the is only one throw.
- If we want the probability of getting the first three
- on the 2nd throw:
- 
+ 

- 
+ Note that the cdf and pdf are identical because the is only one throw.
+ If we want the probability of getting the first three
+ on the 2nd throw:
+ 

-
+

<pre class="programlisting">cout << pdf(g6, 1) << endl; // 0.1389</pre>

- 
-
- 
-
- If we want the probability of getting the first three
- on the 1st or 2nd throw (allowing one failure):
- 
+ 

- 
+ If we want the probability of getting the first three
+ on the 1st or 2nd throw (allowing one failure):
+ 

-
+

<pre class="programlisting">cout << "pdf(g6, 0) + pdf(g6, 1) = " << pdf(g6, 0) + pdf(g6, 1) << endl;</pre>

- 
-
- 
-
- Or more conveniently, and more generally, we can use the Cumulative
- Distribution Function CDF.
- 
+ 

- 
+ Or more conveniently, and more generally, we can use the Cumulative Distribution
+ Function CDF.
+ 

-
+

<pre class="programlisting">cout << "cdf(g6, 1) = " << cdf(g6, 1) << endl; // 0.3056</pre>

- 
-
- 
-
- If we allow many more (12) throws, the probability of getting our
- three gets very high:
- 
+ 

- 
+ If we allow many more (12) throws, the probability of getting our three
+ gets very high:
+ 

-
+

<pre class="programlisting">cout << "cdf(g6, 12) = " << cdf(g6, 12) << endl; // 0.9065 or 90% probability.</pre>

- 
-
- 
-
- If we want to be much more confident, say 99%, we can estimate the
- number of throws to be this sure using the inverse or quantile.
- 
+ 

- 
+ If we want to be much more confident, say 99%, we can estimate the number
+ of throws to be this sure using the inverse or quantile.
+ 

-
+

<pre class="programlisting">cout << "quantile(g6, 0.99) = " << quantile(g6, 0.99) << endl; // 24.26</pre>

- 
-
- 
-
- Note that the value returned is not an integer: if you want an integer
- result you should use either floor, round or ceil functions, or use
- the policies mechanism. See <a class="link" href="../../../policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
- Quantiles of Discrete Distributions</a>
- 
-
- 
+ 

- The geometric distribution is related to the negative binomial    <code class="computeroutput">negative_binomial_distribution(RealType r, RealType
- p);</code>
- with parameter r = 1. So we could get the same
- result using the negative binomial, but using the geometric the results
- will be faster, and may be more accurate.
- 
+ Note that the value returned is not an integer: if you want an integer
+ result you should use either floor, round or ceil functions, or use the
+ policies mechanism. See <a class="link" href="../../../policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
+ Quantiles of Discrete Distributions</a>
+ 

- 
+ The geometric distribution is related to the negative binomial    <code class="computeroutput">negative_binomial_distribution(RealType r, RealType
+ p);</code>
+ with parameter r = 1. So we could get the same result
+ using the negative binomial, but using the geometric the results will
+ be faster, and may be more accurate.
+ 

-
+

<pre class="programlisting">negative_binomial nb(1, success_fraction);
cout << pdf(nb, 1) << endl; // 0.1389
cout << cdf(nb, 1) << endl; // 0.3056</pre>

- 
-
- 
-
- We could also the complement to express the required probability as
- 1 - 0.99 = 0.01 (and get the same result):
- 
+ 

- 
+ We could also the complement to express the required probability as 1
+ - 0.99 = 0.01 (and get the same result):
+ 

-
+

<pre class="programlisting">cout << "quantile(complement(g6, 1 - p)) " << quantile(complement(g6, 0.01)) << endl; // 24.26</pre>

- 
-
- 
-
- Note too that Boost.Math geometric distribution is implemented as a
- continuous function. Unlike other implementations (for example R) it
- uses the number of failures as a
- real parameter, not as an integer.
- If you want this integer behaviour, you may need to enforce this by
- rounding the parameter you pass, probably rounding down, to the nearest
- integer. For example, R returns the success fraction probability for
- all values of failures from 0 to 0.999999 thus:
- 
+ 

-
-
+ Note too that Boost.Math geometric distribution is implemented as a continuous
+ function. Unlike other implementations (for example R) it uses
+ the number of failures as a real parameter,
+ not as an integer. If you want this integer behaviour, you may need to
+ enforce this by rounding the parameter you pass, probably rounding down,
+ to the nearest integer. For example, R returns the success fraction probability
+ for all values of failures from 0 to 0.999999 thus:
+ 
<pre class="programlisting">   R> formatC(pgeom(0.0001,0.5, FALSE), digits=17) " 0.5"
</pre>

- 
-
- So in Boost.Math the equivalent is
- 
-
- 
+ So in Boost.Math the equivalent is
+ 

-
+

<pre class="programlisting"> geometric g05(0.5); // Probability of success = 0.5 or 50%
 // Output all potentially significant digits for the type, here double.
@@ -345,75 +267,52 @@

 cout << cdf(g05, 0.0001) << endl; // returns 0.5000346561579232, not exact 0.5.</pre>

- 
-
- 
-
- To get the R discrete behaviour, you simply need to round with, for
- example, the <code class="computeroutput">floor</code>
- function.
- 
+ 

- 
+ To get the R discrete behaviour, you simply need to round with, for example,
+ the <code class="computeroutput">floor</code> function.
+ 

-
+

<pre class="programlisting">cout << cdf(g05, floor(0.0001)) << endl; // returns exactly 0.5</pre>

- 
-
-
-
+ 
<pre class="programlisting"><code class="computeroutput">> formatC(pgeom(0.9999999,0.5, FALSE), digits=17) [1] " 0.25"</code>
<code class="computeroutput">> formatC(pgeom(1.999999,0.5, FALSE), digits=17)[1] " 0.25" k = 1</code>
<code class="computeroutput">> formatC(pgeom(1.9999999,0.5, FALSE), digits=17)[1] "0.12500000000000003" k = 2</code>
</pre>

- 
+ shows that R makes an arbitrary round-up decision at about 1e7 from the
+ next integer above. This may be convenient in practice, and could be
+ replicated in C++ if desired.
+ 
+<a name="math_toolkit.dist.stat_tut.weg.geometric_eg.surveying_customers_to_find_one_with_a_faulty_product"></a><h6>
+<a name="id1065285"></a>
+ <a class="link" href="geometric_eg.html#math_toolkit.dist.stat_tut.weg.geometric_eg.surveying_customers_to_find_one_with_a_faulty_product">Surveying
+ customers to find one with a faulty product</a>
+ </h6>
+
+ A company knows from warranty claims that 2% of their products will be
+ faulty, so the 'success_fraction' of finding a fault is 0.02. It wants
+ to interview a purchaser of faulty products to assess their 'user experience'.
+ 

- shows that R makes an arbitrary round-up decision at about 1e7 from
- the next integer above. This may be convenient in practice, and could
- be replicated in C++ if desired.
- 
-
- <a name="math_toolkit.dist.stat_tut.weg.geometric_eg.surveying_customers_to_find_one_with_a_faulty_product"></a>
- 
-<h6>
-<a name="id946474"></a>
- <a class="link" href="geometric_eg.html#math_toolkit.dist.stat_tut.weg.geometric_eg.surveying_customers_to_find_one_with_a_faulty_product">Surveying
- customers to find one with a faulty product</a>
- </h6>
-
- 
-
- A company knows from warranty claims that 2% of their products will
- be faulty, so the 'success_fraction' of finding a fault is 0.02. It
- wants to interview a purchaser of faulty products to assess their 'user
- experience'.
- 
-
- 
-
- To estimate how many customers they will probably need to contact in
- order to find one who has suffered from the fault, we first construct
- a geometric distribution with probability 0.02, and then chose a confidence,
- say 80%, 95%, or 99% to finding a customer with a fault. Finally, we
- probably want to round up the result to the integer above using the
- <code class="computeroutput">ceil</code> function. (We
- could also use a policy, but that is hardly worthwhile for this simple
- application.)
- 
-
- 
-
- (This also assumes that each customer only buys one product: if customers
- bought more than one item, the probability of finding a customer with
- a fault obviously improves.)
- 
+ To estimate how many customers they will probably need to contact in
+ order to find one who has suffered from the fault, we first construct
+ a geometric distribution with probability 0.02, and then chose a confidence,
+ say 80%, 95%, or 99% to finding a customer with a fault. Finally, we
+ probably want to round up the result to the integer above using the
+ <code class="computeroutput">ceil</code> function. (We could
+ also use a policy, but that is hardly worthwhile for this simple application.)
+ 

- 
+ (This also assumes that each customer only buys one product: if customers
+ bought more than one item, the probability of finding a customer with
+ a fault obviously improves.)
+ 

-
+

<pre class="programlisting">cout.precision(5);
geometric g(0.02); // On average, 2 in 100 products are faulty.
@@ -432,129 +331,95 @@
 << "% confident of finding we customer with a fault, need to survey "
 << ceil(quantile(g, c)) << " customers." << endl; // 79</pre>

- 
-
- <a name="math_toolkit.dist.stat_tut.weg.geometric_eg.basket_ball_shooters"></a>
- 
-<h6>
-<a name="id947022"></a>
- <a class="link" href="geometric_eg.html#math_toolkit.dist.stat_tut.weg.geometric_eg.basket_ball_shooters">Basket
- Ball Shooters</a>
- </h6>
-
- 
-
- According to Wikipedia, average pro basket ball players get free throws in
- the baskets 70 to 80 % of the time, but some get as high as 95%, and
- others as low as 50%. Suppose we want to compare the probabilities
- of failing to get a score only on the first or on the fifth shot? To
- start we will consider the average shooter, say 75%. So we construct
- a geometric distribution with success_fraction parameter 75/100 = 0.75.
- 
-
- 
+ 
+<a name="math_toolkit.dist.stat_tut.weg.geometric_eg.basket_ball_shooters"></a><h6>
+<a name="id1065832"></a>
+ <a class="link" href="geometric_eg.html#math_toolkit.dist.stat_tut.weg.geometric_eg.basket_ball_shooters">Basket
+ Ball Shooters</a>
+ </h6>
+
+ According to Wikipedia, average pro basket ball players get <a href="http://en.wikipedia.org/wiki/Free_throw" target="_top">free
+ throws</a> in the baskets 70 to 80 % of the time, but some get as
+ high as 95%, and others as low as 50%. Suppose we want to compare the
+ probabilities of failing to get a score only on the first or on the fifth
+ shot? To start we will consider the average shooter, say 75%. So we construct
+ a geometric distribution with success_fraction parameter 75/100 = 0.75.
+ 

-
+

<pre class="programlisting">cout.precision(2);
geometric gav(0.75); // Shooter averages 7.5 out of 10 in the basket.</pre>

- 
-
- 
-
- What is probability of getting 1st try in the basket, that is with
- no failures?
- 
+ 

- 
+ What is probability of getting 1st try in the basket, that is with no
+ failures?
+ 

-
+

<pre class="programlisting">cout << "Probability of score on 1st try = " << pdf(gav, 0) << endl; // 0.75</pre>

- 
-
- 
-
- This is, of course, the success_fraction probability 75%. What is the
- probability that the shooter only scores on the fifth shot? So there
- are 5-1 = 4 failures before the first success.
- 
+ 

- 
+ This is, of course, the success_fraction probability 75%. What is the
+ probability that the shooter only scores on the fifth shot? So there
+ are 5-1 = 4 failures before the first success.
+ 

-
+

<pre class="programlisting">cout << "Probability of score on 5th try = " << pdf(gav, 4) << endl; // 0.0029</pre>

- 
-
- 
-
- Now compare this with the poor and the best players success fraction.
- We need to constructing new distributions with the different success
- fractions, and then get the corresponding probability density functions
- values:
- 
+ 

- 
+ Now compare this with the poor and the best players success fraction.
+ We need to constructing new distributions with the different success
+ fractions, and then get the corresponding probability density functions
+ values:
+ 

-
+

<pre class="programlisting">geometric gbest(0.95);
cout << "Probability of score on 5th try = " << pdf(gbest, 4) << endl; // 5.9e-6
geometric gmediocre(0.50);
cout << "Probability of score on 5th try = " << pdf(gmediocre, 4) << endl; // 0.031</pre>

- 
-
- 
-
- So we can see the very much smaller chance (0.000006) of 4 failures
- by the best shooters, compared to the 0.03 of the mediocre.
- 
-
- <a name="math_toolkit.dist.stat_tut.weg.geometric_eg.estimating_failures"></a>
- 
-<h6>
-<a name="id947416"></a>
- <a class="link" href="geometric_eg.html#math_toolkit.dist.stat_tut.weg.geometric_eg.estimating_failures">Estimating
- failures</a>
- </h6>
-
- 
-
- Of course one man's failure is an other man's success. So a fault can
- be defined as a 'success'.
- 
-
- 
-
- If a fault occurs once after 100 flights, then one might naively say
- that the risk of fault is obviously 1 in 100 = 1/100, a probability
- of 0.01.
- 
+ 

- 
+ So we can see the very much smaller chance (0.000006) of 4 failures by
+ the best shooters, compared to the 0.03 of the mediocre.
+ 
+<a name="math_toolkit.dist.stat_tut.weg.geometric_eg.estimating_failures"></a><h6>
+<a name="id1066227"></a>
+ <a class="link" href="geometric_eg.html#math_toolkit.dist.stat_tut.weg.geometric_eg.estimating_failures">Estimating
+ failures</a>
+ </h6>

- This is the best estimate we can make, but while it is the truth, it
- is not the whole truth, for it hides the big uncertainty when estimating
- from a single event. "One swallow doesn't make a summer."
- To show the magnitude of the uncertainty, the geometric (or the negative
- binomial) distribution can be used.
- 
+ Of course one man's failure is an other man's success. So a fault can
+ be defined as a 'success'.
+ 

- 
+ If a fault occurs once after 100 flights, then one might naively say
+ that the risk of fault is obviously 1 in 100 = 1/100, a probability of
+ 0.01.
+ 

- If we chose the popular 95% confidence in the limits, corresponding
- to an alpha of 0.05, because we are calculating a two-sided interval,
- we must divide alpha by two.
- 
+ This is the best estimate we can make, but while it is the truth, it
+ is not the whole truth, for it hides the big uncertainty when estimating
+ from a single event. "One swallow doesn't make a summer." To
+ show the magnitude of the uncertainty, the geometric (or the negative
+ binomial) distribution can be used.
+ 

- 
+ If we chose the popular 95% confidence in the limits, corresponding to
+ an alpha of 0.05, because we are calculating a two-sided interval, we
+ must divide alpha by two.
+ 

-
+

<pre class="programlisting">double alpha = 0.05;
double k = 100; // So frequency of occurence is 1/100.
@@ -566,19 +431,15 @@
cout << "geometric::find_upper_bound_on_p(" << int(k) << ", " << alpha/2 << ") = "
 << t << endl; // 0.037</pre>

- 
-
- 
-
- So while we estimate the probability is 0.01, it might lie between
- 0.0003 and 0.04. Even if we relax our confidence to alpha = 90%, the
- bounds only contract to 0.0005 and 0.03. And if we require a high confidence,
- they widen to 0.00005 to 0.05.
- 
+ 

- 
+ So while we estimate the probability is 0.01, it might lie between 0.0003
+ and 0.04. Even if we relax our confidence to alpha = 90%, the bounds
+ only contract to 0.0005 and 0.03. And if we require a high confidence,
+ they widen to 0.00005 to 0.05.
+ 

-
+

<pre class="programlisting">alpha = 0.1; // 90% confidence.
t = geometric::find_lower_bound_on_p(k, alpha/2);
@@ -596,24 +457,18 @@
cout << "geometric::find_upper_bound_on_p(" << int(k) << ", " << alpha/2 << ") = "
 << t << endl; // 0.052</pre>

- 
-
- 
-
- In real life, there will usually be more than one event (fault or success),
- when the negative binomial, which has the neccessary extra parameter,
- will be needed.
- 
-
- 
+ 

- As noted above, using a catch block is always a good idea, even if
- you hope not to use it!
- 
+ In real life, there will usually be more than one event (fault or success),
+ when the negative binomial, which has the neccessary extra parameter,
+ will be needed.
+ 

- 
+ As noted above, using a catch block is always a good idea, even if you
+ hope not to use it!
+ 

-
+

<pre class="programlisting">}
catch(const std::exception& e)
@@ -621,27 +476,19 @@
 // an overflow exception should never be thrown.
 std::cout << "\nMessage from thrown exception was:\n " << e.what() << std::endl;</pre>

- 
-
- 
+ 

- For example, without a ignore domain error policy, if we asked for
-
+ For example, without a ignore domain error policy, if we asked for

<pre class="programlisting">pdf(g, -1)</pre>

- for example, we would get an unhelpful abort, but with a catch:
- 
-
-
-
+ for example, we would get an unhelpful abort, but with a catch:
+ 
<pre class="programlisting">Message from thrown exception was:
 Error in function boost::math::pdf(const exponential_distribution<double>&, double):
 Number of failures argument is -1, but must be >= 0 !
</pre>

- 
-
 See full source C++ of this example at geometric_examples.cpp

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 2010-12-22 05:22:56 EST (Wed, 22 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 2010-12-22 05:22:56 EST (Wed, 22 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 2010-12-22 05:22:56 EST (Wed, 22 Dec 2010)
@@ -24,29 +24,23 @@
</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;
@@ -59,17 +53,13 @@
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)
@@ -78,22 +68,16 @@
}
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)
{
@@ -101,43 +85,31 @@
 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 << "]";
 }
@@ -146,24 +118,18 @@
 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>
@@ -180,1154 +146,1150 @@
</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
- 
- &l