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<section id="numpy-random-generator-logistic">
<h1>numpy.random.Generator.logistic<a class="headerlink" href="#numpy-random-generator-logistic" title="Link to this heading">#</a></h1>
<p>method</p>
<dl class="py method">
<dt class="sig sig-object py" id="numpy.random.Generator.logistic">
<span class="sig-prename descclassname"><span class="pre">random.Generator.</span></span><span class="sig-name descname"><span class="pre">logistic</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">loc</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">scale</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">size</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#numpy.random.Generator.logistic" title="Link to this definition">#</a></dt>
<dd><p>Draw samples from a logistic distribution.</p>
<p>Samples are drawn from a logistic distribution with specified
parameters, loc (location or mean, also median), and scale (>0).</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>loc</strong><span class="classifier">float or array_like of floats, optional</span></dt><dd><p>Parameter of the distribution. Default is 0.</p>
</dd>
<dt><strong>scale</strong><span class="classifier">float or array_like of floats, optional</span></dt><dd><p>Parameter of the distribution. Must be non-negative.
Default is 1.</p>
</dd>
<dt><strong>size</strong><span class="classifier">int or tuple of ints, optional</span></dt><dd><p>Output shape. If the given shape is, e.g., <code class="docutils literal notranslate"><span class="pre">(m,</span> <span class="pre">n,</span> <span class="pre">k)</span></code>, then
<code class="docutils literal notranslate"><span class="pre">m</span> <span class="pre">*</span> <span class="pre">n</span> <span class="pre">*</span> <span class="pre">k</span></code> samples are drawn. If size is <code class="docutils literal notranslate"><span class="pre">None</span></code> (default),
a single value is returned if <code class="docutils literal notranslate"><span class="pre">loc</span></code> and <code class="docutils literal notranslate"><span class="pre">scale</span></code> are both scalars.
Otherwise, <code class="docutils literal notranslate"><span class="pre">np.broadcast(loc,</span> <span class="pre">scale).size</span></code> samples are drawn.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>out</strong><span class="classifier">ndarray or scalar</span></dt><dd><p>Drawn samples from the parameterized logistic distribution.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.logistic.html#scipy.stats.logistic" title="(in SciPy v1.15.2)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy.stats.logistic</span></code></a></dt><dd><p>probability density function, distribution or cumulative density function, etc.</p>
</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>The probability density for the Logistic distribution is</p>
<div class="math notranslate nohighlight">
\[P(x) = \frac{e^{-(x-\mu)/s}}{s(1+e^{-(x-\mu)/s})^2},\]</div>
<p>where <span class="math notranslate nohighlight">\(\mu\)</span> = location and <span class="math notranslate nohighlight">\(s\)</span> = scale.</p>
<p>The Logistic distribution is used in Extreme Value problems where it
can act as a mixture of Gumbel distributions, in Epidemiology, and by
the World Chess Federation (FIDE) where it is used in the Elo ranking
system, assuming the performance of each player is a logistically
distributed random variable.</p>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="rccd29a30f060-1" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
<p>Reiss, R.-D. and Thomas M. (2001), “Statistical Analysis of
Extreme Values, from Insurance, Finance, Hydrology and Other
Fields,” Birkhauser Verlag, Basel, pp 132-133.</p>
</div>
<div class="citation" id="rccd29a30f060-2" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></span>
<p>Weisstein, Eric W. “Logistic Distribution.” From
MathWorld–A Wolfram Web Resource.
<a class="reference external" href="https://mathworld.wolfram.com/LogisticDistribution.html">https://mathworld.wolfram.com/LogisticDistribution.html</a></p>
</div>
<div class="citation" id="rccd29a30f060-3" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></span>
<p>Wikipedia, “Logistic-distribution”,
<a class="reference external" href="https://en.wikipedia.org/wiki/Logistic_distribution">https://en.wikipedia.org/wiki/Logistic_distribution</a></p>
</div>
</div>
<p class="rubric">Examples</p>
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<p>Draw samples from the distribution:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">loc</span><span class="p">,</span> <span class="n">scale</span> <span class="o">=</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">1</span>
<span class="gp">>>> </span><span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">s</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">logistic</span><span class="p">(</span><span class="n">loc</span><span class="p">,</span> <span class="n">scale</span><span class="p">,</span> <span class="mi">10000</span><span class="p">)</span>
<span class="gp">>>> </span><span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
<span class="gp">>>> </span><span class="n">count</span><span class="p">,</span> <span class="n">bins</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Sampled data'</span><span class="p">)</span>
</pre></div>
</div>
<p># plot sampled data against the exact distribution</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="k">def</span><span class="w"> </span><span class="nf">logistic</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">loc</span><span class="p">,</span> <span class="n">scale</span><span class="p">):</span>
<span class="gp">... </span> <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">((</span><span class="n">loc</span><span class="o">-</span><span class="n">x</span><span class="p">)</span><span class="o">/</span><span class="n">scale</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">scale</span><span class="o">*</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">((</span><span class="n">loc</span><span class="o">-</span><span class="n">x</span><span class="p">)</span><span class="o">/</span><span class="n">scale</span><span class="p">))</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">logistic_values</span> <span class="o">=</span> <span class="n">logistic</span><span class="p">(</span><span class="n">bins</span><span class="p">,</span> <span class="n">loc</span><span class="p">,</span> <span class="n">scale</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">bin_spacing</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="n">bins</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">bins</span><span class="p">,</span> <span class="n">logistic_values</span> <span class="o">*</span> <span class="n">bin_spacing</span> <span class="o">*</span> <span class="n">s</span><span class="o">.</span><span class="n">size</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Logistic PDF'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
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