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<section id="numpy-random-generator-rayleigh">
<h1>numpy.random.Generator.rayleigh<a class="headerlink" href="#numpy-random-generator-rayleigh" title="Link to this heading">#</a></h1>
<p>method</p>
<dl class="py method">
<dt class="sig sig-object py" id="numpy.random.Generator.rayleigh">
<span class="sig-prename descclassname"><span class="pre">random.Generator.</span></span><span class="sig-name descname"><span class="pre">rayleigh</span></span><span class="sig-paren">(</span><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.rayleigh" title="Link to this definition">#</a></dt>
<dd><p>Draw samples from a Rayleigh distribution.</p>
<p>The <span class="math notranslate nohighlight">\(\chi\)</span> and Weibull distributions are generalizations of the
Rayleigh.</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>scale</strong><span class="classifier">float or array_like of floats, optional</span></dt><dd><p>Scale, also equals the mode. 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">scale</span></code> is a scalar. Otherwise,
<code class="docutils literal notranslate"><span class="pre">np.array(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 Rayleigh distribution.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>The probability density function for the Rayleigh distribution is</p>
<div class="math notranslate nohighlight">
\[P(x;scale) = \frac{x}{scale^2}e^{\frac{-x^2}{2 \cdotp scale^2}}\]</div>
<p>The Rayleigh distribution would arise, for example, if the East
and North components of the wind velocity had identical zero-mean
Gaussian distributions. Then the wind speed would have a Rayleigh
distribution.</p>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="r542a2ef1fe0a-1" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
<p>Brighton Webs Ltd., “Rayleigh Distribution,”
<a class="reference external" href="https://web.archive.org/web/20090514091424/http://brighton-webs.co.uk:80/distributions/rayleigh.asp">https://web.archive.org/web/20090514091424/http://brighton-webs.co.uk:80/distributions/rayleigh.asp</a></p>
</div>
<div class="citation" id="r542a2ef1fe0a-2" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></span>
<p>Wikipedia, “Rayleigh distribution”
<a class="reference external" href="https://en.wikipedia.org/wiki/Rayleigh_distribution">https://en.wikipedia.org/wiki/Rayleigh_distribution</a></p>
</div>
</div>
<p class="rubric">Examples</p>
<div class="try_examples_outer_container docutils container" id="149e3dc4-3ea6-4847-bbad-4ff2f195b421">
<div class="try_examples_button_container"><button class="try_examples_button" onclick="window.tryExamplesShowIframe('149e3dc4-3ea6-4847-bbad-4ff2f195b421','7b0b6d4f-b011-4aec-8d90-b90f54737465','b8a11c74-c1a1-4341-88f3-fcf16c7b39a5','../../../lite/tree/../notebooks/index.html?path=e3b8bf7a_6af0_448a_9d39_575780bbaa1b.ipynb','None')">Try it in your browser!</button></div><div class="try_examples_content docutils container">
<p>Draw values from the distribution and plot the histogram</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="kn">import</span> <span class="n">hist</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">values</span> <span class="o">=</span> <span class="n">hist</span><span class="p">(</span><span class="n">rng</span><span class="o">.</span><span class="n">rayleigh</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">100000</span><span class="p">),</span> <span class="n">bins</span><span class="o">=</span><span class="mi">200</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
</pre></div>
</div>
<p>Wave heights tend to follow a Rayleigh distribution. If the mean wave
height is 1 meter, what fraction of waves are likely to be larger than 3
meters?</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">meanvalue</span> <span class="o">=</span> <span class="mi">1</span>
<span class="gp">>>> </span><span class="n">modevalue</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span> <span class="o">*</span> <span class="n">meanvalue</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">rayleigh</span><span class="p">(</span><span class="n">modevalue</span><span class="p">,</span> <span class="mi">1000000</span><span class="p">)</span>
</pre></div>
</div>
<p>The percentage of waves larger than 3 meters is:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="mf">100.</span><span class="o">*</span><span class="nb">sum</span><span class="p">(</span><span class="n">s</span><span class="o">></span><span class="mi">3</span><span class="p">)</span><span class="o">/</span><span class="mf">1000000.</span>
<span class="go">0.087300000000000003 # random</span>
</pre></div>
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