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  <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) &amp; = &amp; \exp\left(-\left(x+e^{-x}\right)\right)\\ F\left(x\right) &amp; = &amp; \exp\left(-e^{-x}\right)\\ G\left(q\right) &amp; = &amp; -\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 &amp; = &amp; \gamma=-\psi_{0}\left(1\right)\\ \mu_{2} &amp; = &amp; \frac{\pi^{2}}{6}\\ \gamma_{1} &amp; = &amp; \frac{12\sqrt{6}}{\pi^{3}}\zeta\left(3\right)\\ \gamma_{2} &amp; = &amp; \frac{12}{5}\\ m_{d} &amp; = &amp; 0\\ m_{n} &amp; = &amp; -\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>
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