<!DOCTYPE html> <html> <head> <meta charset="utf-8"> <title>Gumbel (LogWeibull, Fisher-Tippetts, Type I Extreme Value) Distribution — SciPy v1.1.0.dev0+4e64658 Reference Guide</title> <link rel="stylesheet" type="text/css" href="../../_static/css/spc-bootstrap.css"> <link rel="stylesheet" type="text/css" href="../../_static/css/spc-extend.css"> <link rel="stylesheet" href="../../_static/scipy.css" type="text/css" > <link rel="stylesheet" href="../../_static/pygments.css" type="text/css" > <script type="text/javascript"> var DOCUMENTATION_OPTIONS = { URL_ROOT: '../../', VERSION: '1.1.0.dev0+4e64658', COLLAPSE_INDEX: false, FILE_SUFFIX: '.html', HAS_SOURCE: false }; </script> <script type="text/javascript" src="../../_static/jquery.js"></script> <script type="text/javascript" src="../../_static/underscore.js"></script> <script type="text/javascript" src="../../_static/doctools.js"></script> <script type="text/javascript" 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href="../../index.html"> <img class="logo" src="../../_static/scipyshiny_small.png" alt="Logo"> </a></p> <h4>Previous topic</h4> <p class="topless"><a href="continuous_gompertz.html" title="previous chapter">Gompertz (Truncated Gumbel) Distribution</a></p> <h4>Next topic</h4> <p class="topless"><a href="continuous_gumbel_l.html" title="next chapter">Gumbel Left-skewed (for minimum order statistic) Distribution</a></p> </div> </div> <div class="span9"> <div class="bodywrapper"> <div class="body" id="spc-section-body"> <div class="section" id="gumbel-logweibull-fisher-tippetts-type-i-extreme-value-distribution"> <span id="continuous-gumbel-r"></span><h1>Gumbel (LogWeibull, Fisher-Tippetts, Type I Extreme Value) Distribution<a class="headerlink" href="#gumbel-logweibull-fisher-tippetts-type-i-extreme-value-distribution" title="Permalink to this headline">ΒΆ</a></h1> <p>One of a class of extreme value distributions (right-skewed).</p> <div class="math"> \begin{eqnarray*} f\left(x\right) & = & \exp\left(-\left(x+e^{-x}\right)\right)\\ F\left(x\right) & = & \exp\left(-e^{-x}\right)\\ G\left(q\right) & = & -\log\left(-\log\left(q\right)\right)\end{eqnarray*}</div><div class="math"> \[M\left(t\right)=\Gamma\left(1-t\right)\]</div> <div class="math"> \begin{eqnarray*} \mu & = & \gamma=-\psi_{0}\left(1\right)\\ \mu_{2} & = & \frac{\pi^{2}}{6}\\ \gamma_{1} & = & \frac{12\sqrt{6}}{\pi^{3}}\zeta\left(3\right)\\ \gamma_{2} & = & \frac{12}{5}\\ m_{d} & = & 0\\ m_{n} & = & -\log\left(\log2\right)\end{eqnarray*}</div><div class="math"> \[h\left[X\right]\approx1.0608407169541684911\]</div> <p>Implementation: <a class="reference internal" href="../../generated/scipy.stats.gumbel_r.html#scipy.stats.gumbel_r" title="scipy.stats.gumbel_r"><code class="xref py py-obj docutils literal"><span class="pre">scipy.stats.gumbel_r</span></code></a></p> </div> </div> </div> </div> </div> </div> </div> <div class="container container-navbar-bottom"> <div class="spc-navbar"> </div> </div> <div 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