diff --git a/doc/distributions/landau.qbk b/doc/distributions/landau.qbk index eca110fb6..b73450504 100644 --- a/doc/distributions/landau.qbk +++ b/doc/distributions/landau.qbk @@ -30,7 +30,7 @@ with shape parameter [alpha]=1, [beta]=1. [@http://en.wikipedia.org/wiki/Probability_distribution probability distribution function PDF] given by: -[equation landau_ref1] +[equation landau_ref1] [/f(x; \mu, c)=\frac{1}{\pi c} \int_{0}^{\infty} \exp(-t) \cos \left( t \left( \frac{x-\mu}{c}\right) + \frac{2t}{\pi} \log \left( \frac{t}{c} \right) \right) dt] The location parameter [mu] is the location of the distribution, while the scale parameter [c] determines the width of the distribution, @@ -97,6 +97,18 @@ The domain of the random variable is \[-[max_value], +[min_value]\]. The error is within 4 epsilon except for the rapidly decaying left tail. +Errors in the PDF at 64-bit double precision: + +[$../graphs/landau_pdf_accuracy_64.png] + +Errors in the CDF at 64-bit double precision: + +[$../graphs/landau_cdf_accuracy_64.png] + +Errors in the CDF-complement at 64-bit double precision: + +[$../graphs/landau_ccdf_accuracy_64.png] + [h4 Implementation] See references. @@ -110,6 +122,7 @@ DOI: 10.36227/techrxiv.171822215.53612870/v2, 2024. [endsect][/section:landau_dist landau] [/ landau.qbk + Copyright Takuma Yoshimura 2024. Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt). diff --git a/doc/equations/landau_ref1.svg b/doc/equations/landau_ref1.svg new file mode 100644 index 000000000..19939a829 --- /dev/null +++ b/doc/equations/landau_ref1.svg @@ -0,0 +1,88 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/doc/graphs/landau_ccdf_accuracy_64.png b/doc/graphs/landau_ccdf_accuracy_64.png new file mode 100644 index 000000000..7e157eb81 Binary files /dev/null and b/doc/graphs/landau_ccdf_accuracy_64.png differ diff --git a/doc/graphs/landau_cdf_accuracy_64.png b/doc/graphs/landau_cdf_accuracy_64.png new file mode 100644 index 000000000..3c4a48eae Binary files /dev/null and b/doc/graphs/landau_cdf_accuracy_64.png differ diff --git a/doc/graphs/landau_pdf1.svg b/doc/graphs/landau_pdf1.svg new file mode 100644 index 000000000..f07e248b1 --- /dev/null +++ b/doc/graphs/landau_pdf1.svg @@ -0,0 +1,1355 @@ + + + + + + + + 2024-07-21T02:07:44.252944 + image/svg+xml + + + Matplotlib v3.9.0, https://matplotlib.org/ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/doc/graphs/landau_pdf2.svg b/doc/graphs/landau_pdf2.svg new file mode 100644 index 000000000..a3a6f7feb --- /dev/null +++ b/doc/graphs/landau_pdf2.svg @@ -0,0 +1,1313 @@ + + + + + + + + 2024-07-21T02:07:43.910893 + image/svg+xml + + + Matplotlib v3.9.0, https://matplotlib.org/ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/doc/graphs/landau_pdf_accuracy_64.png b/doc/graphs/landau_pdf_accuracy_64.png new file mode 100644 index 000000000..3bb84efec Binary files /dev/null and b/doc/graphs/landau_pdf_accuracy_64.png differ