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<a name="Distributions"></a>
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Next: <a href="Random-Number-Generation.html#Random-Number-Generation" accesskey="n" rel="next">Random Number Generation</a>, Previous: <a href="Correlation-and-Regression-Analysis.html#Correlation-and-Regression-Analysis" accesskey="p" rel="prev">Correlation and Regression Analysis</a>, Up: <a href="Statistics.html#Statistics" accesskey="u" rel="up">Statistics</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Distributions-1"></a>
<h3 class="section">26.5 Distributions</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>
<thead><tr><th width="31%">Distribution</th><th width="23%">PDF</th><th width="23%">CDF</th><th width="23%">Quantile</th></tr></thead>
<tr><td width="31%">Univariate Discrete Distribution</td><td width="23%"><code>discrete_pdf</code></td><td width="23%"><code>discrete_cdf</code></td><td width="23%"><code>discrete_inv</code></td></tr>
<tr><td width="31%">Empirical Distribution</td><td width="23%"><code>empirical_pdf</code></td><td width="23%"><code>empirical_cdf</code></td><td width="23%"><code>empirical_inv</code></td></tr>
</table>
<a name="XREFdiscrete_005fpdf"></a><dl>
<dt><a name="index-discrete_005fpdf"></a><em></em> <strong>discrete_pdf</strong> <em>(<var>x</var>, <var>v</var>, <var>p</var>)</em></dt>
<dd><p>For each element of <var>x</var>, compute the probability density function (PDF)
at <var>x</var> of a univariate discrete distribution which assumes the values
in <var>v</var> with probabilities <var>p</var>.
</p></dd></dl>
<a name="XREFdiscrete_005fcdf"></a><dl>
<dt><a name="index-discrete_005fcdf"></a><em></em> <strong>discrete_cdf</strong> <em>(<var>x</var>, <var>v</var>, <var>p</var>)</em></dt>
<dd><p>For each element of <var>x</var>, compute the cumulative distribution function
(CDF) at <var>x</var> of a univariate discrete distribution which assumes the
values in <var>v</var> with probabilities <var>p</var>.
</p></dd></dl>
<a name="XREFdiscrete_005finv"></a><dl>
<dt><a name="index-discrete_005finv"></a><em></em> <strong>discrete_inv</strong> <em>(<var>x</var>, <var>v</var>, <var>p</var>)</em></dt>
<dd><p>For each element of <var>x</var>, compute the quantile (the inverse of the CDF)
at <var>x</var> of the univariate distribution which assumes the values in
<var>v</var> with probabilities <var>p</var>.
</p></dd></dl>
<a name="XREFempirical_005fpdf"></a><dl>
<dt><a name="index-empirical_005fpdf"></a><em></em> <strong>empirical_pdf</strong> <em>(<var>x</var>, <var>data</var>)</em></dt>
<dd><p>For each element of <var>x</var>, compute the probability density function (PDF)
at <var>x</var> of the empirical distribution obtained from the
univariate sample <var>data</var>.
</p></dd></dl>
<a name="XREFempirical_005fcdf"></a><dl>
<dt><a name="index-empirical_005fcdf"></a><em></em> <strong>empirical_cdf</strong> <em>(<var>x</var>, <var>data</var>)</em></dt>
<dd><p>For each element of <var>x</var>, compute the cumulative distribution function
(CDF) at <var>x</var> of the empirical distribution obtained from
the univariate sample <var>data</var>.
</p></dd></dl>
<a name="XREFempirical_005finv"></a><dl>
<dt><a name="index-empirical_005finv"></a><em></em> <strong>empirical_inv</strong> <em>(<var>x</var>, <var>data</var>)</em></dt>
<dd><p>For each element of <var>x</var>, compute the quantile (the inverse of the CDF)
at <var>x</var> of the empirical distribution obtained from the
univariate sample <var>data</var>.
</p></dd></dl>
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