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<h3 class="section" id="Distributions-1"><span>26.5 Distributions<a class="copiable-link" href="#Distributions-1"> ¶</a></span></h3>
<p>Octave has functions for computing the Probability Density Function (PDF), the
Cumulative Distribution function (CDF), and the quantile (the inverse of the
CDF) for arbitrary user-defined distributions (discrete) and for experimental
data (empirical).
</p>
<p>The following table summarizes the supported distributions (in alphabetical
order).
</p>
<table class="multitable">
<thead><tr><th width="31%">Distribution</th><th width="23%">PDF</th><th width="23%">CDF</th><th width="23%">Quantile</th></tr></thead>
<tbody><tr><td width="31%">Univariate Discrete Distribution</td><td width="23%"><code class="code">discrete_pdf</code></td><td width="23%"><code class="code">discrete_cdf</code></td><td width="23%"><code class="code">discrete_inv</code></td></tr>
<tr><td width="31%">Empirical Distribution</td><td width="23%"><code class="code">empirical_pdf</code></td><td width="23%"><code class="code">empirical_cdf</code></td><td width="23%"><code class="code">empirical_inv</code></td></tr>
</tbody>
</table>
<a class="anchor" id="XREFdiscrete_005fpdf"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-discrete_005fpdf"><span><code class="def-type"><var class="var">pdf</var> =</code> <strong class="def-name">discrete_pdf</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">v</var>, <var class="var">p</var>)</code><a class="copiable-link" href="#index-discrete_005fpdf"> ¶</a></span></dt>
<dd><p>For each element of <var class="var">x</var>, compute the probability density function (PDF)
at <var class="var">x</var> of a univariate discrete distribution which assumes the values
in <var class="var">v</var> with probabilities <var class="var">p</var>.
</p></dd></dl>
<a class="anchor" id="XREFdiscrete_005fcdf"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-discrete_005fcdf"><span><code class="def-type"><var class="var">cdf</var> =</code> <strong class="def-name">discrete_cdf</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">v</var>, <var class="var">p</var>)</code><a class="copiable-link" href="#index-discrete_005fcdf"> ¶</a></span></dt>
<dd><p>For each element of <var class="var">x</var>, compute the cumulative distribution function
(CDF) at <var class="var">x</var> of a univariate discrete distribution which assumes the
values in <var class="var">v</var> with probabilities <var class="var">p</var>.
</p></dd></dl>
<a class="anchor" id="XREFdiscrete_005finv"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-discrete_005finv"><span><code class="def-type"><var class="var">q</var> =</code> <strong class="def-name">discrete_inv</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">v</var>, <var class="var">p</var>)</code><a class="copiable-link" href="#index-discrete_005finv"> ¶</a></span></dt>
<dd><p>For each element of <var class="var">x</var>, compute the quantile (the inverse of the CDF)
at <var class="var">x</var> of the univariate distribution which assumes the values in
<var class="var">v</var> with probabilities <var class="var">p</var>.
</p></dd></dl>
<a class="anchor" id="XREFempirical_005fpdf"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-empirical_005fpdf"><span><code class="def-type"><var class="var">pdf</var> =</code> <strong class="def-name">empirical_pdf</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">data</var>)</code><a class="copiable-link" href="#index-empirical_005fpdf"> ¶</a></span></dt>
<dd><p>For each element of <var class="var">x</var>, compute the probability density function (PDF)
at <var class="var">x</var> of the empirical distribution obtained from the
univariate sample <var class="var">data</var>.
</p></dd></dl>
<a class="anchor" id="XREFempirical_005fcdf"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-empirical_005fcdf"><span><code class="def-type"><var class="var">cdf</var> =</code> <strong class="def-name">empirical_cdf</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">data</var>)</code><a class="copiable-link" href="#index-empirical_005fcdf"> ¶</a></span></dt>
<dd><p>For each element of <var class="var">x</var>, compute the cumulative distribution function
(CDF) at <var class="var">x</var> of the empirical distribution obtained from
the univariate sample <var class="var">data</var>.
</p></dd></dl>
<a class="anchor" id="XREFempirical_005finv"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-empirical_005finv"><span><code class="def-type"><var class="var">q</var> =</code> <strong class="def-name">empirical_inv</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">data</var>)</code><a class="copiable-link" href="#index-empirical_005finv"> ¶</a></span></dt>
<dd><p>For each element of <var class="var">x</var>, compute the quantile (the inverse of the CDF)
at <var class="var">x</var> of the empirical distribution obtained from the
univariate sample <var class="var">data</var>.
</p></dd></dl>
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