From 2396fa311c93eced327e1dfaaab00e50bd618009 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 28 Feb 2008 19:12:00 +0000 Subject: [PATCH] Fix mode of the weibull distribution. Add distribution new graphs as PNG and SVG, and change quickbook to reference them. Update dist graph generator. [SVN r43430] --- doc/sf_and_dist/distributions/bernoulli.qbk | 4 +- doc/sf_and_dist/distributions/beta.qbk | 2 +- doc/sf_and_dist/distributions/binomial.qbk | 4 +- doc/sf_and_dist/distributions/cauchy.qbk | 4 +- doc/sf_and_dist/distributions/chi_squared.qbk | 2 +- doc/sf_and_dist/distributions/exponential.qbk | 2 +- .../distributions/extreme_value.qbk | 4 +- doc/sf_and_dist/distributions/fisher.qbk | 2 +- doc/sf_and_dist/distributions/gamma.qbk | 4 +- doc/sf_and_dist/distributions/lognormal.qbk | 4 +- doc/sf_and_dist/distributions/nc_beta.qbk | 2 +- .../distributions/nc_chi_squared.qbk | 2 +- doc/sf_and_dist/distributions/nc_f.qbk | 2 +- doc/sf_and_dist/distributions/nc_t.qbk | 2 +- .../distributions/negative_binomial.qbk | 4 +- doc/sf_and_dist/distributions/normal.qbk | 2 +- doc/sf_and_dist/distributions/pareto.qbk | 11 +- doc/sf_and_dist/distributions/poisson.qbk | 2 +- doc/sf_and_dist/distributions/rayleigh.qbk | 4 +- doc/sf_and_dist/distributions/students_t.qbk | 2 +- doc/sf_and_dist/distributions/triangular.qbk | 4 +- doc/sf_and_dist/distributions/uniform.qbk | 4 +- doc/sf_and_dist/distributions/weibull.qbk | 4 +- doc/sf_and_dist/graphs/acosh.png | Bin 0 -> 21831 bytes doc/sf_and_dist/graphs/asinh.png | Bin 0 -> 19357 bytes doc/sf_and_dist/graphs/atanh.png | Bin 0 -> 18890 bytes doc/sf_and_dist/graphs/bernoulli_cdf.png | Bin 16479 -> 26267 bytes doc/sf_and_dist/graphs/bernoulli_cdf.svg | 66 +++++ doc/sf_and_dist/graphs/bernoulli_pdf.png | Bin 14564 -> 24545 bytes doc/sf_and_dist/graphs/bernoulli_pdf.svg | 63 +++++ doc/sf_and_dist/graphs/beta.png | Bin 5778 -> 33828 bytes doc/sf_and_dist/graphs/beta_pdf.png | Bin 127461 -> 65839 bytes doc/sf_and_dist/graphs/beta_pdf.svg | 78 ++++++ doc/sf_and_dist/graphs/binomial_pdf_1.png | Bin 15775 -> 29384 bytes doc/sf_and_dist/graphs/binomial_pdf_1.svg | 65 +++++ doc/sf_and_dist/graphs/binomial_pdf_2.png | Bin 17896 -> 28535 bytes doc/sf_and_dist/graphs/binomial_pdf_2.svg | 64 +++++ doc/sf_and_dist/graphs/cauchy_pdf1.png | Bin 0 -> 48603 bytes doc/sf_and_dist/graphs/cauchy_pdf1.svg | 59 +++++ doc/sf_and_dist/graphs/cauchy_pdf2.png | Bin 0 -> 44423 bytes doc/sf_and_dist/graphs/cauchy_pdf2.svg | 63 +++++ doc/sf_and_dist/graphs/cbrt.png | Bin 0 -> 17543 bytes doc/sf_and_dist/graphs/chi_squared_pdf.png | Bin 0 -> 39014 bytes doc/sf_and_dist/graphs/chi_squared_pdf.svg | 63 +++++ doc/sf_and_dist/graphs/digamma.png | Bin 6264 -> 25004 bytes doc/sf_and_dist/graphs/dist_graphs.cpp | 241 +++++++++++++++--- doc/sf_and_dist/graphs/erf.png | Bin 0 -> 17137 bytes doc/sf_and_dist/graphs/erf_inv.png | Bin 6422 -> 17754 bytes doc/sf_and_dist/graphs/erfc.png | Bin 0 -> 18536 bytes doc/sf_and_dist/graphs/erfc_inv.png | Bin 7463 -> 20082 bytes doc/sf_and_dist/graphs/expint2.png | Bin 43254 -> 43602 bytes doc/sf_and_dist/graphs/expint_i.png | Bin 21224 -> 21715 bytes doc/sf_and_dist/graphs/expm1.png | Bin 0 -> 19728 bytes doc/sf_and_dist/graphs/exponential_pdf.png | Bin 0 -> 35398 bytes doc/sf_and_dist/graphs/exponential_pdf.svg | 63 +++++ doc/sf_and_dist/graphs/extreme_value_pdf1.png | Bin 0 -> 47602 bytes doc/sf_and_dist/graphs/extreme_value_pdf1.svg | 60 +++++ doc/sf_and_dist/graphs/extreme_value_pdf2.png | Bin 0 -> 47713 bytes doc/sf_and_dist/graphs/extreme_value_pdf2.svg | 63 +++++ doc/sf_and_dist/graphs/fisher_f_pdf.png | Bin 0 -> 52235 bytes doc/sf_and_dist/graphs/fisher_f_pdf.svg | 70 +++++ doc/sf_and_dist/graphs/gamma1_pdf.png | Bin 0 -> 48343 bytes doc/sf_and_dist/graphs/gamma1_pdf.svg | 72 ++++++ doc/sf_and_dist/graphs/gamma2_pdf.png | Bin 0 -> 45314 bytes doc/sf_and_dist/graphs/gamma2_pdf.svg | 63 +++++ doc/sf_and_dist/graphs/gamma_p.png | Bin 5042 -> 38512 bytes doc/sf_and_dist/graphs/gamma_q.png | Bin 5052 -> 39771 bytes doc/sf_and_dist/graphs/ibeta.png | Bin 20426 -> 49856 bytes doc/sf_and_dist/graphs/legendre_p.png | Bin 0 -> 60417 bytes doc/sf_and_dist/graphs/legendre_q.png | Bin 10285 -> 71228 bytes doc/sf_and_dist/graphs/lgamma.png | Bin 4313 -> 26887 bytes doc/sf_and_dist/graphs/log1p.png | Bin 0 -> 14086 bytes doc/sf_and_dist/graphs/lognormal_pdf1.png | Bin 0 -> 36311 bytes doc/sf_and_dist/graphs/lognormal_pdf1.svg | 59 +++++ doc/sf_and_dist/graphs/lognormal_pdf2.png | Bin 0 -> 44803 bytes doc/sf_and_dist/graphs/lognormal_pdf2.svg | 60 +++++ doc/sf_and_dist/graphs/nc_beta_pdf.png | Bin 0 -> 64958 bytes doc/sf_and_dist/graphs/nc_beta_pdf.svg | 84 ++++++ doc/sf_and_dist/graphs/nc_f_pdf.png | Bin 0 -> 57021 bytes doc/sf_and_dist/graphs/nc_f_pdf.svg | 79 ++++++ doc/sf_and_dist/graphs/nc_t_pdf.png | Bin 0 -> 45002 bytes doc/sf_and_dist/graphs/nc_t_pdf.svg | 68 +++++ doc/sf_and_dist/graphs/nccs_pdf.png | Bin 61038 -> 59158 bytes doc/sf_and_dist/graphs/nccs_pdf.svg | 76 ++++++ .../graphs/negative_binomial_pdf_1.png | Bin 0 -> 31736 bytes .../graphs/negative_binomial_pdf_1.svg | 59 +++++ .../graphs/negative_binomial_pdf_2.png | Bin 0 -> 38110 bytes .../graphs/negative_binomial_pdf_2.svg | 66 +++++ doc/sf_and_dist/graphs/normal_pdf.png | Bin 0 -> 52817 bytes doc/sf_and_dist/graphs/normal_pdf.svg | 78 ++++++ doc/sf_and_dist/graphs/pareto_pdf1.png | Bin 0 -> 44205 bytes doc/sf_and_dist/graphs/pareto_pdf1.svg | 63 +++++ doc/sf_and_dist/graphs/pareto_pdf2.png | Bin 0 -> 37721 bytes doc/sf_and_dist/graphs/pareto_pdf2.svg | 62 +++++ doc/sf_and_dist/graphs/poisson_pdf_1.png | Bin 0 -> 26096 bytes doc/sf_and_dist/graphs/poisson_pdf_1.svg | 63 +++++ doc/sf_and_dist/graphs/rayleigh_cdf.png | Bin 24553 -> 43264 bytes doc/sf_and_dist/graphs/rayleigh_cdf.svg | 77 ++++++ doc/sf_and_dist/graphs/rayleigh_pdf.png | Bin 22261 -> 37453 bytes doc/sf_and_dist/graphs/rayleigh_pdf.svg | 72 ++++++ doc/sf_and_dist/graphs/sinc_pi.png | Bin 0 -> 24859 bytes doc/sf_and_dist/graphs/sinhc_pi.png | Bin 0 -> 23613 bytes doc/sf_and_dist/graphs/sqrt1pm1.png | Bin 0 -> 20696 bytes doc/sf_and_dist/graphs/students_t_pdf.png | Bin 0 -> 48363 bytes doc/sf_and_dist/graphs/students_t_pdf.svg | 66 +++++ doc/sf_and_dist/graphs/tgamma.png | Bin 0 -> 25539 bytes doc/sf_and_dist/graphs/tgamma_delta_ratio.png | Bin 0 -> 47842 bytes doc/sf_and_dist/graphs/triangular_cdf.png | Bin 25268 -> 50453 bytes doc/sf_and_dist/graphs/triangular_cdf.svg | 78 ++++++ doc/sf_and_dist/graphs/triangular_pdf.png | Bin 22911 -> 46381 bytes doc/sf_and_dist/graphs/triangular_pdf.svg | 71 ++++++ doc/sf_and_dist/graphs/uniform_cdf.png | Bin 21875 -> 47066 bytes doc/sf_and_dist/graphs/uniform_cdf.svg | 74 ++++++ doc/sf_and_dist/graphs/uniform_pdf.png | Bin 17265 -> 31810 bytes doc/sf_and_dist/graphs/uniform_pdf.svg | 74 ++++++ doc/sf_and_dist/graphs/weibull_pdf1.png | Bin 0 -> 45197 bytes doc/sf_and_dist/graphs/weibull_pdf1.svg | 67 +++++ doc/sf_and_dist/graphs/weibull_pdf2.png | Bin 0 -> 42370 bytes doc/sf_and_dist/graphs/weibull_pdf2.svg | 61 +++++ doc/sf_and_dist/graphs/zeta1.png | Bin 22815 -> 24226 bytes doc/sf_and_dist/graphs/zeta2.png | Bin 22885 -> 24058 bytes doc/sf_and_dist/math.qbk | 9 + include/boost/math/distributions/weibull.hpp | 2 + 123 files changed, 2628 insertions(+), 70 deletions(-) create mode 100644 doc/sf_and_dist/graphs/acosh.png create mode 100644 doc/sf_and_dist/graphs/asinh.png create mode 100644 doc/sf_and_dist/graphs/atanh.png create mode 100644 doc/sf_and_dist/graphs/bernoulli_cdf.svg create mode 100644 doc/sf_and_dist/graphs/bernoulli_pdf.svg create mode 100644 doc/sf_and_dist/graphs/beta_pdf.svg create mode 100644 doc/sf_and_dist/graphs/binomial_pdf_1.svg create mode 100644 doc/sf_and_dist/graphs/binomial_pdf_2.svg create mode 100644 doc/sf_and_dist/graphs/cauchy_pdf1.png create mode 100644 doc/sf_and_dist/graphs/cauchy_pdf1.svg create mode 100644 doc/sf_and_dist/graphs/cauchy_pdf2.png create mode 100644 doc/sf_and_dist/graphs/cauchy_pdf2.svg create mode 100644 doc/sf_and_dist/graphs/cbrt.png create mode 100644 doc/sf_and_dist/graphs/chi_squared_pdf.png create mode 100644 doc/sf_and_dist/graphs/chi_squared_pdf.svg create mode 100644 doc/sf_and_dist/graphs/erf.png create mode 100644 doc/sf_and_dist/graphs/erfc.png create mode 100644 doc/sf_and_dist/graphs/expm1.png create mode 100644 doc/sf_and_dist/graphs/exponential_pdf.png create mode 100644 doc/sf_and_dist/graphs/exponential_pdf.svg create mode 100644 doc/sf_and_dist/graphs/extreme_value_pdf1.png create mode 100644 doc/sf_and_dist/graphs/extreme_value_pdf1.svg create mode 100644 doc/sf_and_dist/graphs/extreme_value_pdf2.png create mode 100644 doc/sf_and_dist/graphs/extreme_value_pdf2.svg create mode 100644 doc/sf_and_dist/graphs/fisher_f_pdf.png create mode 100644 doc/sf_and_dist/graphs/fisher_f_pdf.svg create mode 100644 doc/sf_and_dist/graphs/gamma1_pdf.png create mode 100644 doc/sf_and_dist/graphs/gamma1_pdf.svg create mode 100644 doc/sf_and_dist/graphs/gamma2_pdf.png create mode 100644 doc/sf_and_dist/graphs/gamma2_pdf.svg create mode 100644 doc/sf_and_dist/graphs/legendre_p.png create mode 100644 doc/sf_and_dist/graphs/log1p.png create mode 100644 doc/sf_and_dist/graphs/lognormal_pdf1.png create mode 100644 doc/sf_and_dist/graphs/lognormal_pdf1.svg create mode 100644 doc/sf_and_dist/graphs/lognormal_pdf2.png create mode 100644 doc/sf_and_dist/graphs/lognormal_pdf2.svg create mode 100644 doc/sf_and_dist/graphs/nc_beta_pdf.png create mode 100644 doc/sf_and_dist/graphs/nc_beta_pdf.svg create mode 100644 doc/sf_and_dist/graphs/nc_f_pdf.png create mode 100644 doc/sf_and_dist/graphs/nc_f_pdf.svg create mode 100644 doc/sf_and_dist/graphs/nc_t_pdf.png create mode 100644 doc/sf_and_dist/graphs/nc_t_pdf.svg create mode 100644 doc/sf_and_dist/graphs/nccs_pdf.svg create mode 100644 doc/sf_and_dist/graphs/negative_binomial_pdf_1.png create mode 100644 doc/sf_and_dist/graphs/negative_binomial_pdf_1.svg create mode 100644 doc/sf_and_dist/graphs/negative_binomial_pdf_2.png create mode 100644 doc/sf_and_dist/graphs/negative_binomial_pdf_2.svg create mode 100644 doc/sf_and_dist/graphs/normal_pdf.png create mode 100644 doc/sf_and_dist/graphs/normal_pdf.svg create mode 100644 doc/sf_and_dist/graphs/pareto_pdf1.png create mode 100644 doc/sf_and_dist/graphs/pareto_pdf1.svg create mode 100644 doc/sf_and_dist/graphs/pareto_pdf2.png create mode 100644 doc/sf_and_dist/graphs/pareto_pdf2.svg create mode 100644 doc/sf_and_dist/graphs/poisson_pdf_1.png create mode 100644 doc/sf_and_dist/graphs/poisson_pdf_1.svg create mode 100644 doc/sf_and_dist/graphs/rayleigh_cdf.svg create mode 100644 doc/sf_and_dist/graphs/rayleigh_pdf.svg create mode 100644 doc/sf_and_dist/graphs/sinc_pi.png create mode 100644 doc/sf_and_dist/graphs/sinhc_pi.png create mode 100644 doc/sf_and_dist/graphs/sqrt1pm1.png create mode 100644 doc/sf_and_dist/graphs/students_t_pdf.png create mode 100644 doc/sf_and_dist/graphs/students_t_pdf.svg create mode 100644 doc/sf_and_dist/graphs/tgamma.png create mode 100644 doc/sf_and_dist/graphs/tgamma_delta_ratio.png create mode 100644 doc/sf_and_dist/graphs/triangular_cdf.svg create mode 100644 doc/sf_and_dist/graphs/triangular_pdf.svg create mode 100644 doc/sf_and_dist/graphs/uniform_cdf.svg create mode 100644 doc/sf_and_dist/graphs/uniform_pdf.svg create mode 100644 doc/sf_and_dist/graphs/weibull_pdf1.png create mode 100644 doc/sf_and_dist/graphs/weibull_pdf1.svg create mode 100644 doc/sf_and_dist/graphs/weibull_pdf2.png create mode 100644 doc/sf_and_dist/graphs/weibull_pdf2.svg diff --git a/doc/sf_and_dist/distributions/bernoulli.qbk b/doc/sf_and_dist/distributions/bernoulli.qbk index 17200fb41..d22af07a1 100644 --- a/doc/sf_and_dist/distributions/bernoulli.qbk +++ b/doc/sf_and_dist/distributions/bernoulli.qbk @@ -42,11 +42,11 @@ The following graph illustrates how the [@http://en.wikipedia.org/wiki/Probability_density_function probability density function pdf] varies with the outcome of the single trial: -[$../graphs/bernoulli_pdf.png] +[graph bernoulli_pdf] and the [@http://en.wikipedia.org/wiki/Cumulative_Distribution_Function Cumulative distribution function] -[$../graphs/bernoulli_cdf.png] +[graph bernoulli_cdf] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/beta.qbk b/doc/sf_and_dist/distributions/beta.qbk index 6686ea73c..3a88f925b 100644 --- a/doc/sf_and_dist/distributions/beta.qbk +++ b/doc/sf_and_dist/distributions/beta.qbk @@ -84,7 +84,7 @@ of the shape parameters. Note the [alpha] = [beta] = 2 (blue line) is dome-shaped, and might be approximated by a symmetrical triangular distribution. -[$../graphs/beta_dist.png] +[graph beta_pdf] If [alpha] = [beta] = 1, then it is a __space [@http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29 uniform distribution], diff --git a/doc/sf_and_dist/distributions/binomial.qbk b/doc/sf_and_dist/distributions/binomial.qbk index cad52611d..d790e1708 100644 --- a/doc/sf_and_dist/distributions/binomial.qbk +++ b/doc/sf_and_dist/distributions/binomial.qbk @@ -76,12 +76,12 @@ The following two graphs illustrate how the PDF changes depending upon the distributions parameters, first we'll keep the success fraction /p/ fixed at 0.5, and vary the sample size: -[$../graphs/binomial_pdf_1.png] +[graph binomial_pdf_1] Alternatively, we can keep the sample size fixed at N=20 and vary the success fraction /p/: -[$../graphs/binomial_pdf_2.png] +[graph binomial_pdf_2] [discrete_quantile_warning Binomial] diff --git a/doc/sf_and_dist/distributions/cauchy.qbk b/doc/sf_and_dist/distributions/cauchy.qbk index 34ff68dd1..f56fcbea0 100644 --- a/doc/sf_and_dist/distributions/cauchy.qbk +++ b/doc/sf_and_dist/distributions/cauchy.qbk @@ -44,12 +44,12 @@ of spectral lines. The following graph shows how the distributions moves as the location parameter changes: -[$../graphs/cauchy1.png] +[graph cauchy_pdf1] While the following graph shows how the shape (scale) parameter alters the distribution: -[$../graphs/cauchy2.png] +[graph cauchy_pdf2] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/chi_squared.qbk b/doc/sf_and_dist/distributions/chi_squared.qbk index abc8ec8cd..ed4f208a9 100644 --- a/doc/sf_and_dist/distributions/chi_squared.qbk +++ b/doc/sf_and_dist/distributions/chi_squared.qbk @@ -49,7 +49,7 @@ and has a single parameter [nu][space] that specifies the number of degrees of freedom. The following graph illustrates how the distribution changes for different values of [nu]: -[$../graphs/chi_square.png] +[graph chi_squared_pdf] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/exponential.qbk b/doc/sf_and_dist/distributions/exponential.qbk index 121f2802b..17d923a90 100644 --- a/doc/sf_and_dist/distributions/exponential.qbk +++ b/doc/sf_and_dist/distributions/exponential.qbk @@ -33,7 +33,7 @@ events that happen at a constant average rate. The following graph shows how the distribution changes for different values of the rate parameter lambda: -[$../graphs/exponential_dist.png] +[graph exponential_pdf] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/extreme_value.qbk b/doc/sf_and_dist/distributions/extreme_value.qbk index 2225e9449..5e81eb51e 100644 --- a/doc/sf_and_dist/distributions/extreme_value.qbk +++ b/doc/sf_and_dist/distributions/extreme_value.qbk @@ -51,11 +51,11 @@ f(x) = e[super -x]e[super -e[super -x]] The following graph illustrates how the PDF varies with the location parameter: -[$../graphs/extreme_val_dist.png] +[graph extreme_value_pdf1] And this graph illustrates how the PDF varies with the shape parameter: -[$../graphs/extreme_val_dist2.png] +[graph extreme_value_pdf2] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/fisher.qbk b/doc/sf_and_dist/distributions/fisher.qbk index 7887e2f94..3a4905ca4 100644 --- a/doc/sf_and_dist/distributions/fisher.qbk +++ b/doc/sf_and_dist/distributions/fisher.qbk @@ -41,7 +41,7 @@ has the PDF: The following graph illustrates how the PDF varies depending on the two degrees of freedom parameters. -[$../graphs/fisher_f.png] +[graph fisher_f_pdf] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/gamma.qbk b/doc/sf_and_dist/distributions/gamma.qbk index 1bc233351..9a84c7cb6 100644 --- a/doc/sf_and_dist/distributions/gamma.qbk +++ b/doc/sf_and_dist/distributions/gamma.qbk @@ -61,9 +61,9 @@ parameter], you should pass the reciprocal of the rate as the scale parameter. The following two graphs illustrate how the PDF of the gamma distribution varies as the parameters vary: -[$../graphs/gamma_dist1.png] +[graph gamma1_pdf] -[$../graphs/gamma_dist2.png] +[graph gamma2_pdf] The [*Erlang Distribution] is the same as the Gamma, but with the shape parameter an integer. It is often expressed using a /rate/ rather than a /scale/ as the diff --git a/doc/sf_and_dist/distributions/lognormal.qbk b/doc/sf_and_dist/distributions/lognormal.qbk index 33ac076d6..621da172a 100644 --- a/doc/sf_and_dist/distributions/lognormal.qbk +++ b/doc/sf_and_dist/distributions/lognormal.qbk @@ -43,11 +43,11 @@ parameter on the PDF, note that the range of the random variable remains \[0,+[infin]\] irrespective of the value of the location parameter: -[$../graphs/lognormal1.png] +[graph lognormal_pdf1] The next graph illustrates the effect of the scale parameter on the PDF: -[$../graphs/lognormal2.png] +[graph lognormal_pdf2] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/nc_beta.qbk b/doc/sf_and_dist/distributions/nc_beta.qbk index 6b3b2a704..6f973fb5c 100644 --- a/doc/sf_and_dist/distributions/nc_beta.qbk +++ b/doc/sf_and_dist/distributions/nc_beta.qbk @@ -54,7 +54,7 @@ as: The following graph illustrates how the distribution changes for different values of [lambda]: -[$../graphs/nc_beta_pdf.png] +[graph nc_beta_pdf] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/nc_chi_squared.qbk b/doc/sf_and_dist/distributions/nc_chi_squared.qbk index a1d1e1544..ddf57769a 100644 --- a/doc/sf_and_dist/distributions/nc_chi_squared.qbk +++ b/doc/sf_and_dist/distributions/nc_chi_squared.qbk @@ -66,7 +66,7 @@ where ['f(x;k)] is the central chi-squared distribution PDF, and The following graph illustrates how the distribution changes for different values of [lambda]: -[$../graphs/nccs_pdf.png] +[graph nccs_pdf] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/nc_f.qbk b/doc/sf_and_dist/distributions/nc_f.qbk index 76791ff65..48682b5fd 100644 --- a/doc/sf_and_dist/distributions/nc_f.qbk +++ b/doc/sf_and_dist/distributions/nc_f.qbk @@ -51,7 +51,7 @@ __beta function, or The following graph illustrates how the distribution changes for different values of [lambda]: -[$../graphs/nc_f_pdf.png] +[graph nc_f_pdf] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/nc_t.qbk b/doc/sf_and_dist/distributions/nc_t.qbk index bc1c891e4..b437e1d2b 100644 --- a/doc/sf_and_dist/distributions/nc_t.qbk +++ b/doc/sf_and_dist/distributions/nc_t.qbk @@ -47,7 +47,7 @@ where [sub 1]F[sub 1](a;b;x) is a confluent hypergeometric function. The following graph illustrates how the distribution changes for different values of [delta]: -[$../graphs/nc_t_pdf.png] +[graph nc_t_pdf] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/negative_binomial.qbk b/doc/sf_and_dist/distributions/negative_binomial.qbk index de27bbe7b..5377a4bcd 100644 --- a/doc/sf_and_dist/distributions/negative_binomial.qbk +++ b/doc/sf_and_dist/distributions/negative_binomial.qbk @@ -72,12 +72,12 @@ It has the PDF: The following graph illustrate how the PDF varies as the success fraction /p/ changes: -[$../graphs/neg_binomial_pdf1.png] +[graph negative_binomial_pdf_1] Alternatively, this graph shows how the shape of the PDF varies as the number of successes changes: -[$../graphs/neg_binomial_pdf2.png] +[graph negative_binomial_pdf_2] [h4 Related Distributions] diff --git a/doc/sf_and_dist/distributions/normal.qbk b/doc/sf_and_dist/distributions/normal.qbk index 1b057dd44..b33b5517b 100644 --- a/doc/sf_and_dist/distributions/normal.qbk +++ b/doc/sf_and_dist/distributions/normal.qbk @@ -40,7 +40,7 @@ Given mean [mu][space] and standard deviation [sigma][space] it has the PDF: The variation the PDF with its parameters is illustrated in the following graph: -[$../graphs/normal.png] +[graph normal_pdf] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/pareto.qbk b/doc/sf_and_dist/distributions/pareto.qbk index 040b3c622..82de7fc0e 100644 --- a/doc/sf_and_dist/distributions/pareto.qbk +++ b/doc/sf_and_dist/distributions/pareto.qbk @@ -37,11 +37,14 @@ The [@http://mathworld.wolfram.com/paretoDistribution.html Pareto distribution] often describes the larger compared to the smaller. A classic example is that 80% of the wealth is owned by 20% of the population. -The following graph illustrates how the PDF varies with the shape parameter [alpha]: +The following graph illustrates how the PDF varies with the location parameter [beta]: + +[graph pareto_pdf1] + +And this graph illustrates how the PDF varies with the shape parameter [alpha]: + +[graph pareto_pdf2] -[/$../graphs/paretoShape.png] -[/ TODO produce a graph as png or svg] -[@http://upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Pareto_distributionPDF.png/325px-Pareto_distributionPDF.png Pareto pdf] [h4 Related distributions] diff --git a/doc/sf_and_dist/distributions/poisson.qbk b/doc/sf_and_dist/distributions/poisson.qbk index e65638a97..4e63eef98 100644 --- a/doc/sf_and_dist/distributions/poisson.qbk +++ b/doc/sf_and_dist/distributions/poisson.qbk @@ -41,7 +41,7 @@ for k events, with an expected number of events [lambda]. The following graph illustrates how the PDF varies with the parameter [lambda]: -[$../graphs/poisson.png] +[graph poisson_pdf_1] [discrete_quantile_warning Poisson] diff --git a/doc/sf_and_dist/distributions/rayleigh.qbk b/doc/sf_and_dist/distributions/rayleigh.qbk index 8fa768406..b4e79d700 100644 --- a/doc/sf_and_dist/distributions/rayleigh.qbk +++ b/doc/sf_and_dist/distributions/rayleigh.qbk @@ -40,11 +40,11 @@ or real and imaginary components may have absolute values that are Rayleigh dist The following graph illustrates how the Probability density Function(pdf) varies with the shape parameter [sigma]: -[$../graphs/rayleigh_pdf.png] +[graph rayleigh_pdf] and the Cumulative Distribution Function (cdf) -[$../graphs/rayleigh_cdf.png] +[graph rayleigh_cdf] [h4 Related distributions] diff --git a/doc/sf_and_dist/distributions/students_t.qbk b/doc/sf_and_dist/distributions/students_t.qbk index 25fcdf384..5a6b61032 100644 --- a/doc/sf_and_dist/distributions/students_t.qbk +++ b/doc/sf_and_dist/distributions/students_t.qbk @@ -55,7 +55,7 @@ As the number of degrees of freedom tends towards infinity, then this distribution approaches the normal-distribution. The following graph illustrates how the PDF varies with the degrees of freedom [nu]: -[$../graphs/students_t.png] +[graph students_t_pdf] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/triangular.qbk b/doc/sf_and_dist/distributions/triangular.qbk index eb04ee5a3..4b237f990 100644 --- a/doc/sf_and_dist/distributions/triangular.qbk +++ b/doc/sf_and_dist/distributions/triangular.qbk @@ -72,11 +72,11 @@ The following graph illustrates how the [@http://en.wikipedia.org/wiki/Probability_density_function probability density function PDF] varies with the various parameters: -[$../graphs/triangular_pdf.png] +[graph triangular_pdf] and cumulative distribution function -[$../graphs/triangular_cdf.png] +[graph triangular_cdf] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/uniform.qbk b/doc/sf_and_dist/distributions/uniform.qbk index 098a8d150..5eb664802 100644 --- a/doc/sf_and_dist/distributions/uniform.qbk +++ b/doc/sf_and_dist/distributions/uniform.qbk @@ -61,11 +61,11 @@ The following graph illustrates how the [@http://en.wikipedia.org/wiki/Probability_density_function probability density function PDF] varies with the shape parameter: -[$../graphs/uniform_pdf.png] +[graph uniform_pdf] Likewise for the CDF: -[$../graphs/uniform_cdf.png] +[graph uniform_cdf] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/weibull.qbk b/doc/sf_and_dist/distributions/weibull.qbk index 9530f7534..b0ed6680d 100644 --- a/doc/sf_and_dist/distributions/weibull.qbk +++ b/doc/sf_and_dist/distributions/weibull.qbk @@ -45,11 +45,11 @@ If the failure rate is: The following graph illustrates how the PDF varies with the shape parameter [alpha]: -[$../graphs/weibull.png] +[graph weibull_pdf1] While this graph illustrates how the PDF varies with the scale parameter [beta]: -[$../graphs/weibull2.png] +[graph weibull_pdf2] [h4 Related distributions] diff --git a/doc/sf_and_dist/graphs/acosh.png b/doc/sf_and_dist/graphs/acosh.png new file mode 100644 index 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zC|p=?S3Uc5Ge=DIVuFE%t!?jv&PA*4zt1;P-{r(LA!zNoe53XlQ(w0u=hYgQgB-Hi zbkVI9OfP@^vJwqdT`TJ_IcU{`%m2&QMU@{t#?lr3+OUpw{=eB3Obb4OM&%yq&&=0L zeao=qige1pogx2zUSBGruyj_f#(7VDL5Ih|rxwQCV-D*2bh6sPYo*zyC>^oa!pe*y zC+`TiuQa(A)Nsw0R)uTsUD$M1KVEvEWT z^j~~YLoUZceb*lLB_W%i+Vt)JFL&f)R{PDm7 zS;-KzY8ltOW6{Dg4v&LZJ$RCF4b*-8OuDp{x_rZDb#TQSWsAR2d zZ*Mp846>QsUB;*xx`{2;G3S@vg3z9izrBUmE4=$!HGBQs?Gh7$QnprV&#%)24@7D; zsaY^+hQ`l&z#uh0h>LHw;DUXcQ#U`*_!002Hiy?i_vks7btSv+mfLwgxqS8NRnXYvyLWN(h3`t(J9vFG zdp}>ec4y48npr+-^X+P@Qbp!BDmF~H#qD~4e`()}j}|=79R|HJ9eR5EmB@{VOi0J&i&0Xx^U9rG{ra?PmHs`&{|ta)QAI zPe#q7=iV$S-FW}~?MV*O5}kbD(c`1LZst5Q1C7e;i_vHG0F7WUc&xNKVVQdI@#DuY zU#^U0bnwd6O3(LFNoo$t+87bSe@)$uX+n^U-6FfXKQmtK|NZ;-k1`v%+d2(XlBO@c zeeHkrS(V>UPfveXP*GU;@ynN#$xN)PU-EcbuK#qh#`U6@@nOBNN2P8$OK*Ga?by3N z`&aQs5rw7Sl+yQyJk#zf+q7fy #include +template +struct is_discrete_distribution + : public boost::mpl::false_{}; + +template +struct is_discrete_distribution > + : public boost::mpl::true_{}; +template +struct is_discrete_distribution > + : public boost::mpl::true_{}; +template +struct is_discrete_distribution > + : public boost::mpl::true_{}; +template +struct is_discrete_distribution > + : public boost::mpl::true_{}; + template struct value_finder @@ -43,7 +61,8 @@ template class distribution_plotter { public: - distribution_plotter() : m_min_x(0), m_max_x(0), m_min_y(0), m_max_y(0) {} + distribution_plotter() : m_pdf(true), m_min_x(0), m_max_x(0), m_min_y(0), m_max_y(0) {} + distribution_plotter(bool pdf) : m_pdf(pdf), m_min_x(0), m_max_x(0), m_min_y(0), m_max_y(0) {} void add(const Dist& d, const std::string& name) { @@ -68,9 +87,9 @@ public: { mod = a; } - if(mod <= a) + if((mod <= a) && !is_discrete_distribution::value) { - if(a) + if((a != 0) && (fabs(a) > 1e-2)) mod = a * (1 + 1e-2); else mod = 1e-2; @@ -115,15 +134,18 @@ public: // it's not too close to one end of the graph: // otherwise we may be shooting off to infinity. // - if(mod <= a + (b-a)/50) + if(!is_discrete_distribution::value) { - mod = a + (b-a)/50; + if(mod <= a + (b-a)/50) + { + mod = a + (b-a)/50; + } + if(mod >= b - (b-a)/50) + { + mod = b - (b-a)/50; + } + peek_y = pdf(d, mod); } - if(mod >= b - (b-a)/50) - { - mod = b - (b-a)/50; - } - peek_y = pdf(d, mod); // // Now set our limits: // @@ -156,18 +178,32 @@ public: chartreuse }; + if(m_pdf == false) + { + m_min_y = 0; + m_max_y = 1; + } + svg_2d_plot plot; plot.image_size(750, 400); plot.coord_precision(4); // Avoids any visible steps. plot.title_font_size(20); plot.legend_title_font_size(15); plot.title(title); - plot.legend_on(true).title_on(true); + if((m_distributions.size() == 1) && (m_distributions.begin()->first == "")) + plot.legend_on(false); + else + plot.legend_on(true); + plot.title_on(true); //plot.x_major_labels_on(true).y_major_labels_on(true); - double x_delta = (m_max_x - m_min_x) / 10; + //double x_delta = (m_max_x - m_min_x) / 10; double y_delta = (m_max_y - m_min_y) / 10; - plot.x_range(m_min_x, m_max_x) - .y_range(m_min_y, m_max_y + y_delta); + if(is_discrete_distribution::value) + plot.x_range(m_min_x - 0.5, m_max_x + 0.5) + .y_range(m_min_y, m_max_y + y_delta); + else + plot.x_range(m_min_x, m_max_x) + .y_range(m_min_y, m_max_y + y_delta); plot.x_label_on(true).x_label("Random Variable"); plot.y_label_on(true).y_label("Probability"); plot.plot_border_color(lightslategray) @@ -181,6 +217,11 @@ public: double interval = std::pow(10.0, (int)l); if(((m_max_x - m_min_x) / interval) > 10) interval *= 5; + if(is_discrete_distribution::value) + { + interval = interval > 1 ? std::floor(interval) : 1; + plot.x_num_minor_ticks(0); + } plot.x_major_interval(interval); l = std::floor(std::log10((m_max_y - m_min_y) / 10) + 0.5); interval = std::pow(10.0, (int)l); @@ -190,30 +231,78 @@ public: int color_index = 0; - for(std::list >::const_iterator i = m_distributions.begin(); - i != m_distributions.end(); ++i) + if(!is_discrete_distribution::value) { - double x = m_min_x; - double interval = (m_max_x - m_min_x) / 200; - std::map data; - while(x <= m_max_x) + // + // Continuous distribution: + // + for(std::list >::const_iterator i = m_distributions.begin(); + i != m_distributions.end(); ++i) { - data[x] = pdf(i->second, x); - x += interval; + double x = m_min_x; + double interval = (m_max_x - m_min_x) / 200; + std::map data; + while(x <= m_max_x) + { + data[x] = m_pdf ? pdf(i->second, x) : cdf(i->second, x); + x += interval; + } + plot.plot(data, i->first) + .line_on(true) + .line_color(colors[color_index]) + .line_width(1.) + //.bezier_on(true) // Can't cope with badly behaved like uniform & triangular. + .shape(none); + ++color_index; + color_index = color_index % (sizeof(colors)/sizeof(colors[0])); + } + } + else + { + // + // Discrete distribution: + // + double x_width = 0.75 / m_distributions.size(); + double x_off = -0.5 * 0.75; + for(std::list >::const_iterator i = m_distributions.begin(); + i != m_distributions.end(); ++i) + { + double x = ceil(m_min_x); + double interval = 1; + std::map data; + while(x <= m_max_x) + { + double p; + try{ + p = m_pdf ? pdf(i->second, x) : cdf(i->second, x); + } + catch(const std::domain_error&) + { + p = 0; + } + data[x + x_off] = 0; + data[x + x_off + 0.00001] = p; + data[x + x_off + x_width] = p; + data[x + x_off + x_width + 0.00001] = 0; + x += interval; + } + x_off += x_width; + svg_2d_plot_series& s = plot.plot(data, i->first); + s.line_on(true) + .line_color(colors[color_index]) + .line_width(1.) + //.bezier_on(true) // Can't cope with badly behaved like uniform & triangular. + .shape(none); + s.line_style_.area_fill(colors[color_index]); + ++color_index; + color_index = color_index % (sizeof(colors)/sizeof(colors[0])); } - plot.plot(data, i->first) - .line_on(true) - .line_color(colors[color_index]) - .line_width(1.) - //.bezier_on(true) // Can't cope with badly behaved like uniform & triangular. - .shape(none); - ++color_index; - color_index = color_index % (sizeof(colors)/sizeof(colors[0])); } plot.write(file); } private: + bool m_pdf; std::list > m_distributions; double m_min_x, m_max_x, m_min_y, m_max_y; }; @@ -273,6 +362,15 @@ int main() nc_f_plotter.add(boost::math::non_central_f(10, 20, 100), "v1=10, v2=20, λ=100"); nc_f_plotter.plot("Non Central F PDF", "nc_f_pdf.svg"); + distribution_plotter + nc_t_plotter; + nc_t_plotter.add(boost::math::non_central_t(10, -10), "v=10, δ=-10"); + nc_t_plotter.add(boost::math::non_central_t(10, -5), "v=10, δ=-5"); + nc_t_plotter.add(boost::math::non_central_t(10, 0), "v=10, δ=0"); + nc_t_plotter.add(boost::math::non_central_t(10, 5), "v=10, δ=5"); + nc_t_plotter.add(boost::math::non_central_t(10, 10), "v=10, δ=10"); + nc_t_plotter.plot("Non Central T PDF", "nc_t_pdf.svg"); + distribution_plotter > beta_plotter; beta_plotter.add(boost::math::beta_distribution<>(0.5, 0.5), "alpha=0.5, beta=0.5"); @@ -298,9 +396,10 @@ int main() distribution_plotter > chi_squared_plotter; - chi_squared_plotter.add(boost::math::chi_squared_distribution<>(1), "v=1"); + //chi_squared_plotter.add(boost::math::chi_squared_distribution<>(1), "v=1"); chi_squared_plotter.add(boost::math::chi_squared_distribution<>(2), "v=2"); chi_squared_plotter.add(boost::math::chi_squared_distribution<>(5), "v=5"); + chi_squared_plotter.add(boost::math::chi_squared_distribution<>(10), "v=10"); chi_squared_plotter.plot("Chi Squared Distribution PDF", "chi_squared_pdf.svg"); distribution_plotter > @@ -369,6 +468,15 @@ int main() rayleigh_plotter.add(boost::math::rayleigh_distribution<>(10), "σ=10"); rayleigh_plotter.plot("Rayleigh Distribution PDF", "rayleigh_pdf.svg"); + distribution_plotter > + rayleigh_cdf_plotter(false); + rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(0.5), "σ=0.5"); + rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(1), "σ=1"); + rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(2), "σ=2"); + rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(4), "σ=4"); + rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(10), "σ=10"); + rayleigh_cdf_plotter.plot("Rayleigh Distribution CDF", "rayleigh_cdf.svg"); + distribution_plotter > triangular_plotter; triangular_plotter.add(boost::math::triangular_distribution<>(-1,0,1), "{-1,0,1}"); @@ -378,6 +486,15 @@ int main() triangular_plotter.add(boost::math::triangular_distribution<>(-2,0,3), "{-2,0,3}"); triangular_plotter.plot("Triangular Distribution PDF", "triangular_pdf.svg"); + distribution_plotter > + triangular_cdf_plotter(false); + triangular_cdf_plotter.add(boost::math::triangular_distribution<>(-1,0,1), "{-1,0,1}"); + triangular_cdf_plotter.add(boost::math::triangular_distribution<>(0,1,1), "{0,1,1}"); + triangular_cdf_plotter.add(boost::math::triangular_distribution<>(0,1,3), "{0,1,3}"); + triangular_cdf_plotter.add(boost::math::triangular_distribution<>(0,0.5,1), "{0,0.5,1}"); + triangular_cdf_plotter.add(boost::math::triangular_distribution<>(-2,0,3), "{-2,0,3}"); + triangular_cdf_plotter.plot("Triangular Distribution CDF", "triangular_cdf.svg"); + distribution_plotter > students_t_plotter; students_t_plotter.add(boost::math::students_t_distribution<>(1), "v=1"); @@ -387,9 +504,10 @@ int main() distribution_plotter > weibull_plotter; - weibull_plotter.add(boost::math::weibull_distribution<>(0.2), "shape=0.2"); + weibull_plotter.add(boost::math::weibull_distribution<>(0.75), "shape=0.75"); weibull_plotter.add(boost::math::weibull_distribution<>(1), "shape=1"); weibull_plotter.add(boost::math::weibull_distribution<>(5), "shape=5"); + weibull_plotter.add(boost::math::weibull_distribution<>(10), "shape=10"); weibull_plotter.plot("Weibull Distribution PDF (scale=1)", "weibull_pdf1.svg"); distribution_plotter > @@ -397,7 +515,7 @@ int main() weibull_plotter2.add(boost::math::weibull_distribution<>(3, 0.5), "scale=0.5"); weibull_plotter2.add(boost::math::weibull_distribution<>(3, 1), "scale=1"); weibull_plotter2.add(boost::math::weibull_distribution<>(3, 2), "scale=2"); - weibull_plotter2.plot("weibull Distribution PDF (shape=3)", "weibull_pdf2.svg"); + weibull_plotter2.plot("Weibull Distribution PDF (shape=3)", "weibull_pdf2.svg"); distribution_plotter > uniform_plotter; @@ -407,4 +525,61 @@ int main() uniform_plotter.add(boost::math::uniform_distribution<>(-1, 1), "{-1,1}"); uniform_plotter.plot("Uniform Distribution PDF", "uniform_pdf.svg"); + distribution_plotter > + uniform_cdf_plotter(false); + uniform_cdf_plotter.add(boost::math::uniform_distribution<>(0, 1), "{0,1}"); + uniform_cdf_plotter.add(boost::math::uniform_distribution<>(0, 3), "{0,3}"); + uniform_cdf_plotter.add(boost::math::uniform_distribution<>(-2, 3), "{-2,3}"); + uniform_cdf_plotter.add(boost::math::uniform_distribution<>(-1, 1), "{-1,1}"); + uniform_cdf_plotter.plot("Uniform Distribution CDF", "uniform_cdf.svg"); + + distribution_plotter > + bernoulli_plotter; + bernoulli_plotter.add(boost::math::bernoulli_distribution<>(0.25), "p=0.25"); + bernoulli_plotter.add(boost::math::bernoulli_distribution<>(0.5), "p=0.5"); + bernoulli_plotter.add(boost::math::bernoulli_distribution<>(0.75), "p=0.75"); + bernoulli_plotter.plot("Bernoulli Distribution PDF", "bernoulli_pdf.svg"); + + distribution_plotter > + bernoulli_cdf_plotter(false); + bernoulli_cdf_plotter.add(boost::math::bernoulli_distribution<>(0.25), "p=0.25"); + bernoulli_cdf_plotter.add(boost::math::bernoulli_distribution<>(0.5), "p=0.5"); + bernoulli_cdf_plotter.add(boost::math::bernoulli_distribution<>(0.75), "p=0.75"); + bernoulli_cdf_plotter.plot("Bernoulli Distribution CDF", "bernoulli_cdf.svg"); + + distribution_plotter > + binomial_plotter; + binomial_plotter.add(boost::math::binomial_distribution<>(5, 0.5), "n=5 p=0.5"); + binomial_plotter.add(boost::math::binomial_distribution<>(20, 0.5), "n=20 p=0.5"); + binomial_plotter.add(boost::math::binomial_distribution<>(50, 0.5), "n=50 p=0.5"); + binomial_plotter.plot("Binomial Distribution PDF", "binomial_pdf_1.svg"); + + distribution_plotter > + binomial_plotter2; + binomial_plotter2.add(boost::math::binomial_distribution<>(20, 0.1), "n=20 p=0.1"); + binomial_plotter2.add(boost::math::binomial_distribution<>(20, 0.5), "n=20 p=0.5"); + binomial_plotter2.add(boost::math::binomial_distribution<>(20, 0.9), "n=20 p=0.9"); + binomial_plotter2.plot("Binomial Distribution PDF", "binomial_pdf_2.svg"); + + distribution_plotter > + negative_binomial_plotter; + negative_binomial_plotter.add(boost::math::negative_binomial_distribution<>(20, 0.25), "n=20 p=0.25"); + negative_binomial_plotter.add(boost::math::negative_binomial_distribution<>(20, 0.5), "n=20 p=0.5"); + negative_binomial_plotter.add(boost::math::negative_binomial_distribution<>(20, 0.75), "n=20 p=0.75"); + negative_binomial_plotter.plot("Negative Binomial Distribution PDF", "negative_binomial_pdf_1.svg"); + + distribution_plotter > + negative_binomial_plotter2; + negative_binomial_plotter2.add(boost::math::negative_binomial_distribution<>(10, 0.5), "n=10 p=0.5"); + negative_binomial_plotter2.add(boost::math::negative_binomial_distribution<>(20, 0.5), "n=40 p=0.5"); + negative_binomial_plotter2.add(boost::math::negative_binomial_distribution<>(70, 0.5), "n=70 p=0.5"); + negative_binomial_plotter2.plot("Negative Binomial Distribution PDF", "negative_binomial_pdf_2.svg"); + + distribution_plotter > + poisson_plotter; + poisson_plotter.add(boost::math::poisson_distribution<>(5), "λ=1"); + poisson_plotter.add(boost::math::poisson_distribution<>(10), "λ=10"); + poisson_plotter.add(boost::math::poisson_distribution<>(20), "λ=50"); + poisson_plotter.plot("Poisson Distribution PDF", "poisson_pdf_1.svg"); + } diff --git a/doc/sf_and_dist/graphs/erf.png b/doc/sf_and_dist/graphs/erf.png new file mode 100644 index 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more than one place!] diff --git a/include/boost/math/distributions/weibull.hpp b/include/boost/math/distributions/weibull.hpp index 38e1b3d56..5368b830e 100644 --- a/include/boost/math/distributions/weibull.hpp +++ b/include/boost/math/distributions/weibull.hpp @@ -286,6 +286,8 @@ inline RealType mode(const weibull_distribution& dist) { return result; } + if(shape <= 1) + return 0; result = scale * pow((shape - 1) / shape, 1 / shape); return result; }

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