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<section id="numpy-random-randomstate-noncentral-chisquare">
<h1>numpy.random.RandomState.noncentral_chisquare<a class="headerlink" href="#numpy-random-randomstate-noncentral-chisquare" title="Link to this heading">#</a></h1>
<p>method</p>
<dl class="py method">
<dt class="sig sig-object py" id="numpy.random.RandomState.noncentral_chisquare">
<span class="sig-prename descclassname"><span class="pre">random.RandomState.</span></span><span class="sig-name descname"><span class="pre">noncentral_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">nonc</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.RandomState.noncentral_chisquare" title="Link to this definition">#</a></dt>
<dd><p>Draw samples from a noncentral chi-square distribution.</p>
<p>The noncentral <span class="math notranslate nohighlight">\(\chi^2\)</span> distribution is a generalization of
the <span class="math notranslate nohighlight">\(\chi^2\)</span> distribution.</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.noncentral_chisquare.html#numpy.random.Generator.noncentral_chisquare" title="numpy.random.Generator.noncentral_chisquare"><code class="xref py py-obj docutils literal notranslate"><span class="pre">noncentral_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>Degrees of freedom, must be > 0.</p>
</dd>
<dt><strong>nonc</strong><span class="classifier">float or array_like of floats</span></dt><dd><p>Non-centrality, must be non-negative.</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> and <code class="docutils literal notranslate"><span class="pre">nonc</span></code> are both scalars.
Otherwise, <code class="docutils literal notranslate"><span class="pre">np.broadcast(df,</span> <span class="pre">nonc).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 noncentral chi-square distribution.</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.noncentral_chisquare.html#numpy.random.Generator.noncentral_chisquare" title="numpy.random.Generator.noncentral_chisquare"><code class="xref py py-obj docutils literal notranslate"><span class="pre">random.Generator.noncentral_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 probability density function for the noncentral Chi-square
distribution is</p>
<div class="math notranslate nohighlight">
\[P(x;df,nonc) = \sum^{\infty}_{i=0}
\frac{e^{-nonc/2}(nonc/2)^{i}}{i!}
P_{Y_{df+2i}}(x),\]</div>
<p>where <span class="math notranslate nohighlight">\(Y_{q}\)</span> is the Chi-square with q degrees of freedom.</p>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="rb1ec5a35220a-1" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
<p>Wikipedia, “Noncentral chi-squared distribution”
<a class="reference external" href="https://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution">https://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution</a></p>
</div>
</div>
<p class="rubric">Examples</p>
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<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">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">values</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">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">noncentral_chisquare</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="mi">100000</span><span class="p">),</span>
<span class="gp">... </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>
<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<figure class="align-default">
<img alt="../../../_images/numpy-random-RandomState-noncentral_chisquare-1_00_00.png" class="plot-directive" src="../../../_images/numpy-random-RandomState-noncentral_chisquare-1_00_00.png" />
</figure>
<p>Draw values from a noncentral chisquare with very small noncentrality,
and compare to a chisquare.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">values</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">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">noncentral_chisquare</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mf">.0000001</span><span class="p">,</span> <span class="mi">100000</span><span class="p">),</span>
<span class="gp">... </span> <span class="n">bins</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">0.</span><span class="p">,</span> <span class="mi">25</span><span class="p">,</span> <span class="mf">.1</span><span class="p">),</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">values2</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">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">3</span><span class="p">,</span> <span class="mi">100000</span><span class="p">),</span>
<span class="gp">... </span> <span class="n">bins</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">0.</span><span class="p">,</span> <span class="mi">25</span><span class="p">,</span> <span class="mf">.1</span><span class="p">),</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</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">values</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">0</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">values</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">-</span><span class="n">values2</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="s1">'ob'</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>
</div>
<figure class="align-default">
<img alt="../../../_images/numpy-random-RandomState-noncentral_chisquare-1_01_00.png" class="plot-directive" src="../../../_images/numpy-random-RandomState-noncentral_chisquare-1_01_00.png" />
</figure>
<p>Demonstrate how large values of non-centrality lead to a more symmetric
distribution.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">values</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">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">noncentral_chisquare</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="mi">100000</span><span class="p">),</span>
<span class="gp">... </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>
<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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