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<section id="numpy-random-chisquare">
<h1>numpy.random.chisquare<a class="headerlink" href="#numpy-random-chisquare" title="Link to this heading">#</a></h1>
<dl class="py function">
<dt class="sig sig-object py" id="numpy.random.chisquare">
<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">chisquare</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">df</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.chisquare" title="Link to this definition">#</a></dt>
<dd><p>Draw samples from a chi-square distribution.</p>
<p>When <em class="xref py py-obj">df</em> independent random variables, each with standard normal
distributions (mean 0, variance 1), are squared and summed, the
resulting distribution is chi-square (see Notes). This distribution
is often used in hypothesis testing.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>New code should use the <a class="reference internal" href="numpy.random.Generator.chisquare.html#numpy.random.Generator.chisquare" title="numpy.random.Generator.chisquare"><code class="xref py py-obj docutils literal notranslate"><span class="pre">chisquare</span></code></a>
method of a <a class="reference internal" href="../generator.html#numpy.random.Generator" title="numpy.random.Generator"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Generator</span></code></a> instance instead;
please see the <a class="reference internal" href="../index.html#random-quick-start"><span class="std std-ref">Quick start</span></a>.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>df</strong><span class="classifier">float or array_like of floats</span></dt><dd><p>Number of degrees of freedom, must be > 0.</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">df</span></code> is a scalar. Otherwise,
<code class="docutils literal notranslate"><span class="pre">np.array(df).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 chi-square distribution.</p>
</dd>
</dl>
</dd>
<dt class="field-odd">Raises<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt>ValueError</dt><dd><p>When <em class="xref py py-obj">df</em> <= 0 or when an inappropriate <a class="reference internal" href="../../generated/numpy.size.html#numpy.size" title="numpy.size"><code class="xref py py-obj docutils literal notranslate"><span class="pre">size</span></code></a> (e.g. <code class="docutils literal notranslate"><span class="pre">size=-1</span></code>)
is given.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="numpy.random.Generator.chisquare.html#numpy.random.Generator.chisquare" title="numpy.random.Generator.chisquare"><code class="xref py py-obj docutils literal notranslate"><span class="pre">random.Generator.chisquare</span></code></a></dt><dd><p>which should be used for new code.</p>
</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>The variable obtained by summing the squares of <em class="xref py py-obj">df</em> independent,
standard normally distributed random variables:</p>
<div class="math notranslate nohighlight">
\[Q = \sum_{i=1}^{\mathtt{df}} X^2_i\]</div>
<p>is chi-square distributed, denoted</p>
<div class="math notranslate nohighlight">
\[Q \sim \chi^2_k.\]</div>
<p>The probability density function of the chi-squared distribution is</p>
<div class="math notranslate nohighlight">
\[p(x) = \frac{(1/2)^{k/2}}{\Gamma(k/2)}
x^{k/2 - 1} e^{-x/2},\]</div>
<p>where <span class="math notranslate nohighlight">\(\Gamma\)</span> is the gamma function,</p>
<div class="math notranslate nohighlight">
\[\Gamma(x) = \int_0^{-\infty} t^{x - 1} e^{-t} dt.\]</div>
<p class="rubric">References</p>
<div role="list" class="citation-list">
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<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
<p>NIST “Engineering Statistics Handbook”
<a class="reference external" href="https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm">https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm</a></p>
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<p class="rubric">Examples</p>
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<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">chisquare</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">)</span>
<span class="go">array([ 1.89920014, 9.00867716, 3.13710533, 5.62318272]) # random</span>
</pre></div>
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