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  <div class="section" id="scipy-stats-argus">
<h1>scipy.stats.argus<a class="headerlink" href="#scipy-stats-argus" title="Permalink to this headline">¶</a></h1>
<dl class="data">
<dt id="scipy.stats.argus">
<code class="descclassname">scipy.stats.</code><code class="descname">argus</code><em class="property"> = &lt;scipy.stats._continuous_distns.argus_gen object&gt;</em><a class="reference external" href="https://github.com/scipy/scipy/blob/4e64658/scipy/stats/_continuous_distns.py"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#scipy.stats.argus" title="Permalink to this definition">¶</a></dt>
<dd><p>Argus distribution</p>
<p>As an instance of the <a class="reference internal" href="scipy.stats.rv_continuous.html#scipy.stats.rv_continuous" title="scipy.stats.rv_continuous"><code class="xref py py-obj docutils literal"><span class="pre">rv_continuous</span></code></a> class, <a class="reference internal" href="#scipy.stats.argus" title="scipy.stats.argus"><code class="xref py py-obj docutils literal"><span class="pre">argus</span></code></a> object inherits from it
a collection of generic methods (see below for the full list),
and completes them with details specific for this particular distribution.</p>
<p class="rubric">Notes</p>
<p>The probability density function for <a class="reference internal" href="#scipy.stats.argus" title="scipy.stats.argus"><code class="xref py py-obj docutils literal"><span class="pre">argus</span></code></a> is:</p>
<div class="math">
\[ \begin{align}\begin{aligned}f(x, \chi) = \frac{\chi^3}{\sqrt{2\pi} \Psi(\chi)} x \sqrt{1-x^2}
             \exp(- 0.5 \chi^2 (1 - x^2))\\where:\end{aligned}\end{align} \]</div>
<div class="math">
\[\Psi(\chi) = \Phi(\chi) - \chi \phi(\chi) - 1/2\]</div>
<p>with <span class="math">\(\Phi\)</span> and <span class="math">\(\phi\)</span> being the CDF and PDF of a standard
normal distribution, respectively.</p>
<p><a class="reference internal" href="#scipy.stats.argus" title="scipy.stats.argus"><code class="xref py py-obj docutils literal"><span class="pre">argus</span></code></a> takes <span class="math">\(\chi\)</span> as shape a parameter.</p>
<p class="rubric">References</p>
<table class="docutils citation" frame="void" id="r576" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id1">[R576]</a></td><td>“ARGUS distribution”,
<a class="reference external" href="https://en.wikipedia.org/wiki/ARGUS_distribution">https://en.wikipedia.org/wiki/ARGUS_distribution</a></td></tr>
</tbody>
</table>
<p>The probability density above is defined in the “standardized” form. To shift
and/or scale the distribution use the <code class="docutils literal"><span class="pre">loc</span></code> and <code class="docutils literal"><span class="pre">scale</span></code> parameters.
Specifically, <code class="docutils literal"><span class="pre">argus.pdf(x,</span> <span class="pre">chi,</span> <span class="pre">loc,</span> <span class="pre">scale)</span></code> is identically
equivalent to <code class="docutils literal"><span class="pre">argus.pdf(y,</span> <span class="pre">chi)</span> <span class="pre">/</span> <span class="pre">scale</span></code> with
<code class="docutils literal"><span class="pre">y</span> <span class="pre">=</span> <span class="pre">(x</span> <span class="pre">-</span> <span class="pre">loc)</span> <span class="pre">/</span> <span class="pre">scale</span></code>.</p>
<div class="versionadded">
<p><span class="versionmodified">New in version 0.19.0.</span></p>
</div>
<p class="rubric">Examples</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">scipy.stats</span> <span class="k">import</span> <span class="n">argus</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
</pre></div>
</div>
<p>Calculate a few first moments:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">chi</span> <span class="o">=</span> <span class="mi">1</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">mean</span><span class="p">,</span> <span class="n">var</span><span class="p">,</span> <span class="n">skew</span><span class="p">,</span> <span class="n">kurt</span> <span class="o">=</span> <span class="n">argus</span><span class="o">.</span><span class="n">stats</span><span class="p">(</span><span class="n">chi</span><span class="p">,</span> <span class="n">moments</span><span class="o">=</span><span class="s1">&#39;mvsk&#39;</span><span class="p">)</span>
</pre></div>
</div>
<p>Display the probability density function (<code class="docutils literal"><span class="pre">pdf</span></code>):</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </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="n">argus</span><span class="o">.</span><span class="n">ppf</span><span class="p">(</span><span class="mf">0.01</span><span class="p">,</span> <span class="n">chi</span><span class="p">),</span>
<span class="gp">... </span>                <span class="n">argus</span><span class="o">.</span><span class="n">ppf</span><span class="p">(</span><span class="mf">0.99</span><span class="p">,</span> <span class="n">chi</span><span class="p">),</span> <span class="mi">100</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">ax</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">argus</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">chi</span><span class="p">),</span>
<span class="gp">... </span>       <span class="s1">&#39;r-&#39;</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.6</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;argus pdf&#39;</span><span class="p">)</span>
</pre></div>
</div>
<p>Alternatively, the distribution object can be called (as a function)
to fix the shape, location and scale parameters. This returns a “frozen”
RV object holding the given parameters fixed.</p>
<p>Freeze the distribution and display the frozen <code class="docutils literal"><span class="pre">pdf</span></code>:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">rv</span> <span class="o">=</span> <span class="n">argus</span><span class="p">(</span><span class="n">chi</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">ax</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">rv</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">x</span><span class="p">),</span> <span class="s1">&#39;k-&#39;</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;frozen pdf&#39;</span><span class="p">)</span>
</pre></div>
</div>
<p>Check accuracy of <code class="docutils literal"><span class="pre">cdf</span></code> and <code class="docutils literal"><span class="pre">ppf</span></code>:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">vals</span> <span class="o">=</span> <span class="n">argus</span><span class="o">.</span><span class="n">ppf</span><span class="p">([</span><span class="mf">0.001</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.999</span><span class="p">],</span> <span class="n">chi</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">allclose</span><span class="p">([</span><span class="mf">0.001</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.999</span><span class="p">],</span> <span class="n">argus</span><span class="o">.</span><span class="n">cdf</span><span class="p">(</span><span class="n">vals</span><span class="p">,</span> <span class="n">chi</span><span class="p">))</span>
<span class="go">True</span>
</pre></div>
</div>
<p>Generate random numbers:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">r</span> <span class="o">=</span> <span class="n">argus</span><span class="o">.</span><span class="n">rvs</span><span class="p">(</span><span class="n">chi</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="mi">1000</span><span class="p">)</span>
</pre></div>
</div>
<p>And compare the histogram:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">ax</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">normed</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">histtype</span><span class="o">=</span><span class="s1">&#39;stepfilled&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s1">&#39;best&#39;</span><span class="p">,</span> <span class="n">frameon</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<div class="figure">
<img alt="../_images/scipy-stats-argus-1.png" src="../_images/scipy-stats-argus-1.png" />
</div>
<p class="rubric">Methods</p>
<table border="1" class="docutils">
<colgroup>
<col width="51%" />
<col width="49%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td><code class="docutils literal"><span class="pre">rvs(chi,</span> <span class="pre">loc=0,</span> <span class="pre">scale=1,</span> <span class="pre">size=1,</span> <span class="pre">random_state=None)</span></code></td>
<td>Random variates.</td>
</tr>
<tr class="row-even"><td><code class="docutils literal"><span class="pre">pdf(x,</span> <span class="pre">chi,</span> <span class="pre">loc=0,</span> <span class="pre">scale=1)</span></code></td>
<td>Probability density function.</td>
</tr>
<tr class="row-odd"><td><code class="docutils literal"><span class="pre">logpdf(x,</span> <span class="pre">chi,</span> <span class="pre">loc=0,</span> <span class="pre">scale=1)</span></code></td>
<td>Log of the probability density function.</td>
</tr>
<tr class="row-even"><td><code class="docutils literal"><span class="pre">cdf(x,</span> <span class="pre">chi,</span> <span class="pre">loc=0,</span> <span class="pre">scale=1)</span></code></td>
<td>Cumulative distribution function.</td>
</tr>
<tr class="row-odd"><td><code class="docutils literal"><span class="pre">logcdf(x,</span> <span class="pre">chi,</span> <span class="pre">loc=0,</span> <span class="pre">scale=1)</span></code></td>
<td>Log of the cumulative distribution function.</td>
</tr>
<tr class="row-even"><td><code class="docutils literal"><span class="pre">sf(x,</span> <span class="pre">chi,</span> <span class="pre">loc=0,</span> <span class="pre">scale=1)</span></code></td>
<td>Survival function  (also defined as <code class="docutils literal"><span class="pre">1</span> <span class="pre">-</span> <span class="pre">cdf</span></code>, but <em class="xref py py-obj">sf</em> is sometimes more accurate).</td>
</tr>
<tr class="row-odd"><td><code class="docutils literal"><span class="pre">logsf(x,</span> <span class="pre">chi,</span> <span class="pre">loc=0,</span> <span class="pre">scale=1)</span></code></td>
<td>Log of the survival function.</td>
</tr>
<tr class="row-even"><td><code class="docutils literal"><span class="pre">ppf(q,</span> <span class="pre">chi,</span> <span class="pre">loc=0,</span> <span class="pre">scale=1)</span></code></td>
<td>Percent point function (inverse of <code class="docutils literal"><span class="pre">cdf</span></code> — percentiles).</td>
</tr>
<tr class="row-odd"><td><code class="docutils literal"><span class="pre">isf(q,</span> <span class="pre">chi,</span> <span class="pre">loc=0,</span> <span class="pre">scale=1)</span></code></td>
<td>Inverse survival function (inverse of <code class="docutils literal"><span class="pre">sf</span></code>).</td>
</tr>
<tr class="row-even"><td><code class="docutils literal"><span class="pre">moment(n,</span> <span class="pre">chi,</span> <span class="pre">loc=0,</span> <span class="pre">scale=1)</span></code></td>
<td>Non-central moment of order n</td>
</tr>
<tr class="row-odd"><td><code class="docutils literal"><span class="pre">stats(chi,</span> <span class="pre">loc=0,</span> <span class="pre">scale=1,</span> <span class="pre">moments='mv')</span></code></td>
<td>Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).</td>
</tr>
<tr class="row-even"><td><code class="docutils literal"><span class="pre">entropy(chi,</span> <span class="pre">loc=0,</span> <span class="pre">scale=1)</span></code></td>
<td>(Differential) entropy of the RV.</td>
</tr>
<tr class="row-odd"><td><code class="docutils literal"><span class="pre">fit(data,</span> <span class="pre">chi,</span> <span class="pre">loc=0,</span> <span class="pre">scale=1)</span></code></td>
<td>Parameter estimates for generic data.</td>
</tr>
<tr class="row-even"><td><code class="docutils literal"><span class="pre">expect(func,</span> <span class="pre">args=(chi,),</span> <span class="pre">loc=0,</span> <span class="pre">scale=1,</span> <span class="pre">lb=None,</span> <span class="pre">ub=None,</span> <span class="pre">conditional=False,</span> <span class="pre">**kwds)</span></code></td>
<td>Expected value of a function (of one argument) with respect to the distribution.</td>
</tr>
<tr class="row-odd"><td><code class="docutils literal"><span class="pre">median(chi,</span> <span class="pre">loc=0,</span> <span class="pre">scale=1)</span></code></td>
<td>Median of the distribution.</td>
</tr>
<tr class="row-even"><td><code class="docutils literal"><span class="pre">mean(chi,</span> <span class="pre">loc=0,</span> <span class="pre">scale=1)</span></code></td>
<td>Mean of the distribution.</td>
</tr>
<tr class="row-odd"><td><code class="docutils literal"><span class="pre">var(chi,</span> <span class="pre">loc=0,</span> <span class="pre">scale=1)</span></code></td>
<td>Variance of the distribution.</td>
</tr>
<tr class="row-even"><td><code class="docutils literal"><span class="pre">std(chi,</span> <span class="pre">loc=0,</span> <span class="pre">scale=1)</span></code></td>
<td>Standard deviation of the distribution.</td>
</tr>
<tr class="row-odd"><td><code class="docutils literal"><span class="pre">interval(alpha,</span> <span class="pre">chi,</span> <span class="pre">loc=0,</span> <span class="pre">scale=1)</span></code></td>
<td>Endpoints of the range that contains alpha percent of the distribution</td>
</tr>
</tbody>
</table>
</dd></dl>

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