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<section id="numpy-random-generator-weibull">
<h1>numpy.random.Generator.weibull<a class="headerlink" href="#numpy-random-generator-weibull" title="Link to this heading">#</a></h1>
<p>method</p>
<dl class="py method">
<dt class="sig sig-object py" id="numpy.random.Generator.weibull">
<span class="sig-prename descclassname"><span class="pre">random.Generator.</span></span><span class="sig-name descname"><span class="pre">weibull</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</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.weibull" title="Link to this definition">#</a></dt>
<dd><p>Draw samples from a Weibull distribution.</p>
<p>Draw samples from a 1-parameter Weibull distribution with the given
shape parameter <em class="xref py py-obj">a</em>.</p>
<div class="math notranslate nohighlight">
\[X = (-ln(U))^{1/a}\]</div>
<p>Here, U is drawn from the uniform distribution over (0,1].</p>
<p>The more common 2-parameter Weibull, including a scale parameter
<span class="math notranslate nohighlight">\(\lambda\)</span> is just <span class="math notranslate nohighlight">\(X = \lambda(-ln(U))^{1/a}\)</span>.</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>a</strong><span class="classifier">float or array_like of floats</span></dt><dd><p>Shape parameter of the distribution. Must be nonnegative.</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">a</span></code> is a scalar. Otherwise,
<code class="docutils literal notranslate"><span class="pre">np.array(a).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 Weibull 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.weibull_max.html#scipy.stats.weibull_max" title="(in SciPy v1.15.2)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy.stats.weibull_max</span></code></a></dt><dd></dd>
<dt><a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.weibull_min.html#scipy.stats.weibull_min" title="(in SciPy v1.15.2)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy.stats.weibull_min</span></code></a></dt><dd></dd>
<dt><a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.genextreme.html#scipy.stats.genextreme" title="(in SciPy v1.15.2)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy.stats.genextreme</span></code></a></dt><dd></dd>
<dt><a class="reference internal" href="numpy.random.Generator.gumbel.html#numpy.random.Generator.gumbel" title="numpy.random.Generator.gumbel"><code class="xref py py-obj docutils literal notranslate"><span class="pre">gumbel</span></code></a></dt><dd></dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>The Weibull (or Type III asymptotic extreme value distribution
for smallest values, SEV Type III, or Rosin-Rammler
distribution) is one of a class of Generalized Extreme Value
(GEV) distributions used in modeling extreme value problems.
This class includes the Gumbel and Frechet distributions.</p>
<p>The probability density for the Weibull distribution is</p>
<div class="math notranslate nohighlight">
\[p(x) = \frac{a}
{\lambda}(\frac{x}{\lambda})^{a-1}e^{-(x/\lambda)^a},\]</div>
<p>where <span class="math notranslate nohighlight">\(a\)</span> is the shape and <span class="math notranslate nohighlight">\(\lambda\)</span> the scale.</p>
<p>The function has its peak (the mode) at
<span class="math notranslate nohighlight">\(\lambda(\frac{a-1}{a})^{1/a}\)</span>.</p>
<p>When <code class="docutils literal notranslate"><span class="pre">a</span> <span class="pre">=</span> <span class="pre">1</span></code>, the Weibull distribution reduces to the exponential
distribution.</p>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="r6c241f843c17-1" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
<p>Waloddi Weibull, Royal Technical University, Stockholm,
1939 “A Statistical Theory Of The Strength Of Materials”,
Ingeniorsvetenskapsakademiens Handlingar Nr 151, 1939,
Generalstabens Litografiska Anstalts Forlag, Stockholm.</p>
</div>
<div class="citation" id="r6c241f843c17-2" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></span>
<p>Waloddi Weibull, “A Statistical Distribution Function of
Wide Applicability”, Journal Of Applied Mechanics ASME Paper
1951.</p>
</div>
<div class="citation" id="r6c241f843c17-3" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></span>
<p>Wikipedia, “Weibull distribution”,
<a class="reference external" href="https://en.wikipedia.org/wiki/Weibull_distribution">https://en.wikipedia.org/wiki/Weibull_distribution</a></p>
</div>
</div>
<p class="rubric">Examples</p>
<div class="try_examples_outer_container docutils container" id="18ea88f0-61d2-428f-a0a1-9df3d7e199fb">
<div class="try_examples_button_container"><button class="try_examples_button" onclick="window.tryExamplesShowIframe('18ea88f0-61d2-428f-a0a1-9df3d7e199fb','c4bf6965-dd95-48c9-838e-d8968648b45e','dfea0259-0cf1-494e-9200-d31183385d63','../../../lite/tree/../notebooks/index.html?path=7a1cffb2_d48a_4e7e_b3b9_7b488338c4de.ipynb','None')">Try it in your browser!</button></div><div class="try_examples_content docutils container">
<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">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">a</span> <span class="o">=</span> <span class="mf">5.</span> <span class="c1"># shape</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">weibull</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
</pre></div>
</div>
<p>Display the histogram of the samples, along with
the probability density function:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></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="k">def</span><span class="w"> </span><span class="nf">weibull</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">a</span><span class="p">):</span>
<span class="gp">... </span> <span class="k">return</span> <span class="p">(</span><span class="n">a</span> <span class="o">/</span> <span class="n">n</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">x</span> <span class="o">/</span> <span class="n">n</span><span class="p">)</span><span class="o">**</span><span class="p">(</span><span class="n">a</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</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="o">-</span><span class="p">(</span><span class="n">x</span> <span class="o">/</span> <span class="n">n</span><span class="p">)</span><span class="o">**</span><span class="n">a</span><span class="p">)</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">rng</span><span class="o">.</span><span class="n">weibull</span><span class="p">(</span><span class="mf">5.</span><span class="p">,</span> <span class="mi">1000</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1000</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">x</span><span class="p">,</span> <span class="n">weibull</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="mf">1.</span><span class="p">,</span> <span class="mf">5.</span><span class="p">)</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">'Weibull 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>
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