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<title>GNU Scientific Library &ndash; Reference Manual: The Pareto Distribution</title>

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<a name="The-Pareto-Distribution"></a>
<div class="header">
<p>
Next: <a href="Spherical-Vector-Distributions.html#Spherical-Vector-Distributions" accesskey="n" rel="next">Spherical Vector Distributions</a>, Previous: <a href="The-Logistic-Distribution.html#The-Logistic-Distribution" accesskey="p" rel="previous">The Logistic Distribution</a>, Up: <a href="Random-Number-Distributions.html#Random-Number-Distributions" accesskey="u" rel="up">Random Number Distributions</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="The-Pareto-Distribution-1"></a>
<h3 class="section">20.23 The Pareto Distribution</h3>
<dl>
<dt><a name="index-gsl_005fran_005fpareto"></a>Function: <em>double</em> <strong>gsl_ran_pareto</strong> <em>(const gsl_rng * <var>r</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dd><a name="index-Pareto-distribution"></a>
<p>This function returns a random variate from the Pareto distribution of
order <var>a</var>.  The distribution function is,
</p>
<div class="example">
<pre class="example">p(x) dx = (a/b) / (x/b)^{a+1} dx
</pre></div>

<p>for <em>x &gt;= b</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fran_005fpareto_005fpdf"></a>Function: <em>double</em> <strong>gsl_ran_pareto_pdf</strong> <em>(double <var>x</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dd><p>This function computes the probability density <em>p(x)</em> at <var>x</var>
for a Pareto distribution with exponent <var>a</var> and scale <var>b</var>, using
the formula given above.
</p></dd></dl>

<br>

<dl>
<dt><a name="index-gsl_005fcdf_005fpareto_005fP"></a>Function: <em>double</em> <strong>gsl_cdf_pareto_P</strong> <em>(double <var>x</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fpareto_005fQ"></a>Function: <em>double</em> <strong>gsl_cdf_pareto_Q</strong> <em>(double <var>x</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fpareto_005fPinv"></a>Function: <em>double</em> <strong>gsl_cdf_pareto_Pinv</strong> <em>(double <var>P</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fpareto_005fQinv"></a>Function: <em>double</em> <strong>gsl_cdf_pareto_Qinv</strong> <em>(double <var>Q</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dd><p>These functions compute the cumulative distribution functions
<em>P(x)</em>, <em>Q(x)</em> and their inverses for the Pareto
distribution with exponent <var>a</var> and scale <var>b</var>.
</p></dd></dl>




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