diff options
| author | Anas Nashif <anas.nashif@intel.com> | 2013-08-26 08:15:55 -0400 |
|---|---|---|
| committer | Anas Nashif <anas.nashif@intel.com> | 2013-08-26 08:15:55 -0400 |
| commit | bb4dd8289b351fae6b55e303f189127a394a1edd (patch) | |
| tree | 77c9c35a31b1459dd7988c2448e797d142530c41 /libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists | |
| parent | 1a78a62555be32868418fe52f8e330c9d0f95d5a (diff) | |
| download | boost-bb4dd8289b351fae6b55e303f189127a394a1edd.tar.gz boost-bb4dd8289b351fae6b55e303f189127a394a1edd.tar.bz2 boost-bb4dd8289b351fae6b55e303f189127a394a1edd.zip | |
Imported Upstream version 1.51.0upstream/1.51.0
Diffstat (limited to 'libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists')
31 files changed, 565 insertions, 37 deletions
diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html index 5ab7051942..cf96ccaeab 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html @@ -343,7 +343,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html index 2a6e62cb14..bbc7f3cb5d 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html @@ -612,7 +612,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html index aa63813786..faae0f690d 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html @@ -904,7 +904,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html index a5ac5d19c6..8d19fa1b19 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html @@ -294,7 +294,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html index efb1c53cf0..133854cc84 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html @@ -400,7 +400,7 @@ independent, normally distributed random <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html index 358bee87f3..5f1fc10835 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html @@ -318,7 +318,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html index 192428d78a..b4e1b90e8a 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html @@ -320,7 +320,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html index c0f7b8d5f6..05a0f6a21e 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html @@ -427,7 +427,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html index 50c2c5e0f9..d4bfb8b27a 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html @@ -361,7 +361,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/geometric_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/geometric_dist.html index b1a590d0d6..fe09827a1f 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/geometric_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/geometric_dist.html @@ -849,7 +849,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html index b9618b26bf..5ab8ced41f 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html @@ -328,7 +328,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html index 8401701fb7..2436766a37 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html @@ -467,7 +467,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html index 819d0d49db..0a9f625a97 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html @@ -364,7 +364,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html index cae96d473d..16dc6afcad 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html @@ -437,7 +437,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html index 5d64ef71e3..66a30cf10f 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html @@ -350,7 +350,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html index 9acd51d751..e3c1e1c2e6 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html @@ -286,7 +286,7 @@ as special cases if RealType <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html index b972a86879..d1f4705754 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html @@ -318,7 +318,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html index fc01557454..a04e51808b 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html @@ -402,7 +402,7 @@ is a central χ<sup>2</sup> random variable with <span class="emphasis"><em> <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html index 52fbca511c..2a8271538d 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html @@ -500,7 +500,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html index ab4515e896..84603934b0 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html @@ -402,7 +402,7 @@ is the non-centrality parameter, <span class="emphasis"><em>x</em></span> is the <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html index 18e2927b83..db8f62d9aa 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html @@ -351,7 +351,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html index 83795f9c54..66794effd6 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html @@ -894,7 +894,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html index 50a9668e52..33143f1354 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html @@ -68,7 +68,7 @@ Given mean μ  and standard deviation σ  it has the PDF: </p> <p> - <span class="inlinemediaobject"><img src="../../../../../equations/normal_ref1.png"></span> +   <span class="inlinemediaobject"><img src="../../../../../equations/normal_ref1.png"></span> </p> <p> The variation the PDF with its parameters is illustrated in the following @@ -77,6 +77,18 @@ <p> <span class="inlinemediaobject"><img src="../../../../../graphs/normal_pdf.png" align="middle"></span> </p> +<p> + The cumulative distribution function is given by + </p> +<p> +   <span class="inlinemediaobject"><img src="../../../../../equations/normal_cdf.png"></span> + </p> +<p> + and illustrated by this graph + </p> +<p> + <span class="inlinemediaobject"><img src="../../../../../graphs/normal_cdf.png" align="middle"></span> + </p> <h5> <a name="math_toolkit.dist.dist_ref.dists.normal_dist.h0"></a> <span><a name="math_toolkit.dist.dist_ref.dists.normal_dist.member_functions"></a></span><a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.member_functions">Member @@ -250,6 +262,18 @@ <tr> <td> <p> + median + </p> + </td> +<td> + <p> + The same as the mean. + </p> + </td> +</tr> +<tr> +<td> + <p> skewness </p> </td> @@ -289,7 +313,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html index b28ab91dc8..2a7331a6fd 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html @@ -340,7 +340,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html index 5d6ea4a081..5f7b4d590d 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html @@ -320,7 +320,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html index 878eec68d6..0663b5d26d 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html @@ -7,7 +7,7 @@ <link rel="home" href="../../../../index.html" title="Math Toolkit"> <link rel="up" href="../dists.html" title="Distributions"> <link rel="prev" href="poisson_dist.html" title="Poisson Distribution"> -<link rel="next" href="students_t_dist.html" title="Students t Distribution"> +<link rel="next" href="skew_normal_dist.html" title="Skew Normal Distribution"> </head> <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> <table cellpadding="2" width="100%"><tr> @@ -20,7 +20,7 @@ </tr></table> <hr> <div class="spirit-nav"> -<a accesskey="p" href="poisson_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="students_t_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a> +<a accesskey="p" href="poisson_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="skew_normal_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a> </div> <div class="section math_toolkit_dist_dist_ref_dists_rayleigh"> <div class="titlepage"><div><div><h5 class="title"> @@ -336,7 +336,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> @@ -344,7 +344,7 @@ </tr></table> <hr> <div class="spirit-nav"> -<a accesskey="p" href="poisson_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="students_t_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a> +<a accesskey="p" href="poisson_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="skew_normal_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a> </div> </body> </html> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/skew_normal_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/skew_normal_dist.html new file mode 100644 index 0000000000..73bd8b63b3 --- /dev/null +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/skew_normal_dist.html @@ -0,0 +1,504 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Skew Normal Distribution</title> +<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.76.1"> +<link rel="home" href="../../../../index.html" title="Math Toolkit"> +<link rel="up" href="../dists.html" title="Distributions"> +<link rel="prev" href="rayleigh.html" title="Rayleigh Distribution"> +<link rel="next" href="students_t_dist.html" title="Students t Distribution"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../../../boost.png"></td> +<td align="center"><a href="../../../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="rayleigh.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="students_t_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section math_toolkit_dist_dist_ref_dists_skew_normal_dist"> +<div class="titlepage"><div><div><h5 class="title"> +<a name="math_toolkit.dist.dist_ref.dists.skew_normal_dist"></a><a class="link" href="skew_normal_dist.html" title="Skew Normal Distribution">Skew + Normal Distribution</a> +</h5></div></div></div> +<p> +</p> +<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">skew_normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre> +<p> + </p> +<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> + <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span> +<span class="keyword">class</span> <span class="identifier">skew_normal_distribution</span><span class="special">;</span> + +<span class="keyword">typedef</span> <span class="identifier">skew_normal_distribution</span><span class="special"><></span> <span class="identifier">normal</span><span class="special">;</span> + +<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">></span> +<span class="keyword">class</span> <span class="identifier">skew_normal_distribution</span> +<span class="special">{</span> +<span class="keyword">public</span><span class="special">:</span> + <span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span> + <span class="keyword">typedef</span> <span class="identifier">Policy</span> <span class="identifier">policy_type</span><span class="special">;</span> + <span class="comment">// Constructor:</span> + <span class="identifier">skew_normal_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">location</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">shape</span> <span class="special">=</span> <span class="number">0</span><span class="special">);</span> + <span class="comment">// Accessors:</span> + <span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> <span class="comment">// mean if normal.</span> + <span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> <span class="comment">// width, standard deviation if normal.</span> + <span class="identifier">RealType</span> <span class="identifier">shape</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> <span class="comment">// The distribution is right skewed if shape > 0 and is left skewed if shape < 0.</span> + <span class="comment">// The distribution is normal if shape is zero.</span> +<span class="special">};</span> + +<span class="special">}}</span> <span class="comment">// namespaces</span> +</pre> +<p> + The skew normal distribution is a variant of the most well known Gaussian + statistical distribution. + </p> +<p> + The skew normal distribution with shape zero resembles the <a href="http://en.wikipedia.org/wiki/Normal_distribution" target="_top">Normal + Distribution</a>, hence the latter can be regarded as a special case + of the more generic skew normal distribution. + </p> +<p> + If the standard (mean = 0, scale = 1) normal distribution probability + density function is + </p> +<p> +     <span class="inlinemediaobject"><img src="../../../../../equations/normal01_pdf.png"></span> + </p> +<p> + and the cumulative distribution function + </p> +<p> +     <span class="inlinemediaobject"><img src="../../../../../equations/normal01_cdf.png"></span> + </p> +<p> + then the <a href="http://en.wikipedia.org/wiki/Probability_density_function" target="_top">PDF</a> + of the <a href="http://en.wikipedia.org/wiki/Skew_normal_distribution" target="_top">skew + normal distribution</a> with shape parameter α, defined by O'Hagan + and Leonhard (1976) is + </p> +<p> +     <span class="inlinemediaobject"><img src="../../../../../equations/skew_normal_pdf0.png"></span> + </p> +<p> + Given <a href="http://en.wikipedia.org/wiki/Location_parameter" target="_top">location</a> + ξ, <a href="http://en.wikipedia.org/wiki/Scale_parameter" target="_top">scale</a> + ω, and <a href="http://en.wikipedia.org/wiki/Shape_parameter" target="_top">shape</a> + α, it can be <a href="http://en.wikipedia.org/wiki/Skew_normal_distribution" target="_top">transformed</a>, + to the form: + </p> +<p> +     <span class="inlinemediaobject"><img src="../../../../../equations/skew_normal_pdf.png"></span> + </p> +<p> + and <a href="http://en.wikipedia.org/wiki/Cumulative_distribution_function" target="_top">CDF</a>: + </p> +<p> +     <span class="inlinemediaobject"><img src="../../../../../equations/skew_normal_cdf.png"></span> + </p> +<p> + where <span class="emphasis"><em>T(h,a)</em></span> is Owen's T function, and <span class="emphasis"><em>Φ(x)</em></span> + is the normal distribution. + </p> +<p> + The variation the PDF and CDF with its parameters is illustrated in the + following graphs: + </p> +<p> + <span class="inlinemediaobject"><img src="../../../../../graphs/skew_normal_pdf.png" align="middle"></span> + <span class="inlinemediaobject"><img src="../../../../../graphs/skew_normal_cdf.png" align="middle"></span> + </p> +<h5> +<a name="math_toolkit.dist.dist_ref.dists.skew_normal_dist.h0"></a> + <span><a name="math_toolkit.dist.dist_ref.dists.skew_normal_dist.member_functions"></a></span><a class="link" href="skew_normal_dist.html#math_toolkit.dist.dist_ref.dists.skew_normal_dist.member_functions">Member + Functions</a> + </h5> +<pre class="programlisting"><span class="identifier">skew_normal_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">location</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">shape</span> <span class="special">=</span> <span class="number">0</span><span class="special">);</span> +</pre> +<p> + Constructs a skew_normal distribution with location ξ, scale ω and shape + α. + </p> +<p> + Requires scale > 0, otherwise <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a> + is called. + </p> +<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> +</pre> +<p> + returns the location ξ of this distribution, + </p> +<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> +</pre> +<p> + returns the scale ω of this distribution, + </p> +<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">shape</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> +</pre> +<p> + returns the shape α of this distribution. + </p> +<p> + (Location and scale function match other similar distributions, allowing + the functions <code class="computeroutput"><span class="identifier">find_location</span></code> + and <code class="computeroutput"><span class="identifier">find_scale</span></code> to be + used generically). + </p> +<div class="note"><table border="0" summary="Note"> +<tr> +<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../../../doc/src/images/note.png"></td> +<th align="left">Note</th> +</tr> +<tr><td align="left" valign="top"> +<p> + While the shape parameter may be chosen arbitrarily (finite), the resulting + <span class="bold"><strong>skewness</strong></span> of the distribution is in + fact limited to about (-1, 1); strictly, the interval is (-0.9952717, + 0.9952717). + </p> +<p> + A parameter δ is related to the shape α by δ = α / (1 + α²), and used in the + expression for skewness <span class="inlinemediaobject"><img src="../../../../../equations/skew_normal_skewness.png"></span> + + </p> +</td></tr> +</table></div> +<h5> +<a name="math_toolkit.dist.dist_ref.dists.skew_normal_dist.h1"></a> + <span><a name="math_toolkit.dist.dist_ref.dists.skew_normal_dist.references"></a></span><a class="link" href="skew_normal_dist.html#math_toolkit.dist.dist_ref.dists.skew_normal_dist.references">References</a> + </h5> +<div class="itemizedlist"><ul class="itemizedlist" type="disc"> +<li class="listitem"> + <a href="http://azzalini.stat.unipd.it/SN/" target="_top">Skew-Normal Probability + Distribution</a> for many links and bibliography. + </li> +<li class="listitem"> + <a href="http://azzalini.stat.unipd.it/SN/Intro/intro.html" target="_top">A + very brief introduction to the skew-normal distribution</a> by + Adelchi Azzalini (2005-11-2). + </li> +<li class="listitem"> + See a <a href="http://www.tri.org.au/azzalini.html" target="_top">skew-normal + function animation</a>. + </li> +</ul></div> +<h5> +<a name="math_toolkit.dist.dist_ref.dists.skew_normal_dist.h2"></a> + <span><a name="math_toolkit.dist.dist_ref.dists.skew_normal_dist.non_member_accessors"></a></span><a class="link" href="skew_normal_dist.html#math_toolkit.dist.dist_ref.dists.skew_normal_dist.non_member_accessors">Non-member + Accessors</a> + </h5> +<p> + All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member + accessor functions</a> that are generic to all distributions are supported: + <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>, + <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard + Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>, + <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>, + <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>, + <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>, + <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>, + <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>. + </p> +<p> + The domain of the random variable is <span class="emphasis"><em>-[max_value</em></span>, + +[min_value]]. Infinite values are not supported. + </p> +<p> + There are no <a href="http://en.wikipedia.org/wiki/Closed-form_expression" target="_top">closed-form + expression</a> known for the mode and median, but these are computed + for the + </p> +<div class="itemizedlist"><ul class="itemizedlist" type="disc"> +<li class="listitem"> + mode - by finding the maximum of the PDF. + </li> +<li class="listitem"> + median - by computing <code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="number">1</span><span class="special">/</span><span class="number">2</span><span class="special">)</span></code>. + </li> +</ul></div> +<p> + The maximum of the PDF is sought through searching the root of f'(x)=0. + </p> +<p> + Both involve iterative methods that will have lower accuracy than other + estimates. + </p> +<h5> +<a name="math_toolkit.dist.dist_ref.dists.skew_normal_dist.h3"></a> + <span><a name="math_toolkit.dist.dist_ref.dists.skew_normal_dist.testing"></a></span><a class="link" href="skew_normal_dist.html#math_toolkit.dist.dist_ref.dists.skew_normal_dist.testing">Testing</a> + </h5> +<p> + <a href="http://www.r-project.org/" target="_top">The R Project for Statistical + Computing</a> using library(sn) described at <a href="http://azzalini.stat.unipd.it/SN/" target="_top">Skew-Normal + Probability Distribution</a>, and at <a href="http://cran.r-project.org/web/packages/sn/sn.pd" target="_top">R + skew-normal(sn) package</a>. + </p> +<p> + Package sn provides functions related to the skew-normal (SN) and the + skew-t (ST) probability distributions, both for the univariate and for + the the multivariate case, including regression models. + </p> +<p> + <a href="http://www.wolfram.com/products/mathematica/index.html" target="_top">Wolfram + Mathematica</a> was also used to generate some more accurate spot + test data. + </p> +<h5> +<a name="math_toolkit.dist.dist_ref.dists.skew_normal_dist.h4"></a> + <span><a name="math_toolkit.dist.dist_ref.dists.skew_normal_dist.accuracy"></a></span><a class="link" href="skew_normal_dist.html#math_toolkit.dist.dist_ref.dists.skew_normal_dist.accuracy">Accuracy</a> + </h5> +<p> + The skew_normal distribution with shape = zero is implemented as a special + case, equivalent to the normal distribution in terms of the <a class="link" href="../../../special/sf_erf/error_function.html" title="Error Functions">error + function</a>, and therefore should have excellent accuracy. + </p> +<p> + The PDF and mean, variance, skewness and kurtosis are also accurately + evaluated using <a href="http://en.wikipedia.org/wiki/Analytical_expression" target="_top">analytical + expressions</a>. The CDF requires <a href="http://en.wikipedia.org/wiki/Owen%27s_T_function" target="_top">Owen's + T function</a> that is evaluated using a Boost C++ <a class="link" href="../../../special/owens_t.html" title="Owen's T function">Owens + T</a> implementation of the algorithms of M. Patefield and D. Tandy, + Journal of Statistical Software, 5(5), 1-25 (2000); the complicated accuracy + of this function is discussed in detail at <a class="link" href="../../../special/owens_t.html" title="Owen's T function">Owens + T</a>. + </p> +<p> + The median and mode are calculated by iterative root finding, and both + will be less accurate. + </p> +<h5> +<a name="math_toolkit.dist.dist_ref.dists.skew_normal_dist.h5"></a> + <span><a name="math_toolkit.dist.dist_ref.dists.skew_normal_dist.implementation"></a></span><a class="link" href="skew_normal_dist.html#math_toolkit.dist.dist_ref.dists.skew_normal_dist.implementation">Implementation</a> + </h5> +<p> + In the following table, ξ is the location of the distribution, and ω is its + scale, and α is its shape. + </p> +<div class="informaltable"><table class="table"> +<colgroup> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Function + </p> + </th> +<th> + <p> + Implementation Notes + </p> + </th> +</tr></thead> +<tbody> +<tr> +<td> + <p> + pdf + </p> + </td> +<td> + <p> + Using: <span class="inlinemediaobject"><img src="../../../../../equations/skew_normal_pdf.png"></span> + </p> + </td> +</tr> +<tr> +<td> + <p> + cdf + </p> + </td> +<td> + <p> + Using: <span class="inlinemediaobject"><img src="../../../../../equations/skew_normal_cdf.png"></span><br> where <span class="emphasis"><em>T(h,a)</em></span> + is Owen's T function, and <span class="emphasis"><em>Φ(x)</em></span> is the normal + distribution. + </p> + </td> +</tr> +<tr> +<td> + <p> + cdf complement + </p> + </td> +<td> + <p> + Using: complement of normal distribution + 2 * Owens_t + </p> + </td> +</tr> +<tr> +<td> + <p> + quantile + </p> + </td> +<td> + <p> + Maximum of the pdf is sought through searching the root of + f'(x)=0 + </p> + </td> +</tr> +<tr> +<td> + <p> + quantile from the complement + </p> + </td> +<td> + <p> + -quantile(SN(-location ξ, scale ω, -shapeα), p) + </p> + </td> +</tr> +<tr> +<td> + <p> + location + </p> + </td> +<td> + <p> + location ξ + </p> + </td> +</tr> +<tr> +<td> + <p> + scale + </p> + </td> +<td> + <p> + scale ω + </p> + </td> +</tr> +<tr> +<td> + <p> + shape + </p> + </td> +<td> + <p> + shape α + </p> + </td> +</tr> +<tr> +<td> + <p> + median + </p> + </td> +<td> + <p> + quantile(1/2) + </p> + </td> +</tr> +<tr> +<td> + <p> + mean + </p> + </td> +<td> + <p> + <span class="inlinemediaobject"><img src="../../../../../equations/skew_normal_mean.png"></span> + </p> + </td> +</tr> +<tr> +<td> + <p> + mode + </p> + </td> +<td> + <p> + Maximum of the pdf is sought through searching the root of + f'(x)=0 + </p> + </td> +</tr> +<tr> +<td> + <p> + variance + </p> + </td> +<td> + <p> + <span class="inlinemediaobject"><img src="../../../../../equations/skew_normal_variance.png"></span> + </p> + </td> +</tr> +<tr> +<td> + <p> + skewness + </p> + </td> +<td> + <p> + <span class="inlinemediaobject"><img src="../../../../../equations/skew_normal_skewness.png"></span> + </p> + </td> +</tr> +<tr> +<td> + <p> + kurtosis + </p> + </td> +<td> + <p> + kurtosis excess-3 + </p> + </td> +</tr> +<tr> +<td> + <p> + kurtosis excess + </p> + </td> +<td> + <p> + <span class="inlinemediaobject"><img src="../../../../../equations/skew_normal_kurt_ex.png"></span> + </p> + </td> +</tr> +</tbody> +</table></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="rayleigh.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="students_t_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html index c205b592c5..40df64738c 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html @@ -6,7 +6,7 @@ <meta name="generator" content="DocBook XSL Stylesheets V1.76.1"> <link rel="home" href="../../../../index.html" title="Math Toolkit"> <link rel="up" href="../dists.html" title="Distributions"> -<link rel="prev" href="rayleigh.html" title="Rayleigh Distribution"> +<link rel="prev" href="skew_normal_dist.html" title="Skew Normal Distribution"> <link rel="next" href="triangular_dist.html" title="Triangular Distribution"> </head> <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> @@ -20,7 +20,7 @@ </tr></table> <hr> <div class="spirit-nav"> -<a accesskey="p" href="rayleigh.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="triangular_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a> +<a accesskey="p" href="skew_normal_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="triangular_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a> </div> <div class="section math_toolkit_dist_dist_ref_dists_students_t_dist"> <div class="titlepage"><div><div><h5 class="title"> @@ -408,7 +408,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> @@ -416,7 +416,7 @@ </tr></table> <hr> <div class="spirit-nav"> -<a accesskey="p" href="rayleigh.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="triangular_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a> +<a accesskey="p" href="skew_normal_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="triangular_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a> </div> </body> </html> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html index c804517fc0..977829a0bf 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html @@ -414,7 +414,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/uniform_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/uniform_dist.html index 4f9c377609..76bcfddd0c 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/uniform_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/uniform_dist.html @@ -357,7 +357,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> diff --git a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/weibull_dist.html b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/weibull_dist.html index a77f8fc3e1..4e210c1cdc 100644 --- a/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/weibull_dist.html +++ b/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/weibull_dist.html @@ -357,7 +357,7 @@ <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno - Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<p> + Lalande, Johan Råde, Gautam Sewani, Thijs van den Berg and Benjamin Sobotta<p> Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) </p> |