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

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<a name="The-Rayleigh-Distribution"></a>
<div class="header">
<p>
Next: <a href="The-Rayleigh-Tail-Distribution.html#The-Rayleigh-Tail-Distribution" accesskey="n" rel="next">The Rayleigh Tail Distribution</a>, Previous: <a href="The-Cauchy-Distribution.html#The-Cauchy-Distribution" accesskey="p" rel="previous">The Cauchy 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-Rayleigh-Distribution-1"></a>
<h3 class="section">20.10 The Rayleigh Distribution</h3>
<dl>
<dt><a name="index-gsl_005fran_005frayleigh"></a>Function: <em>double</em> <strong>gsl_ran_rayleigh</strong> <em>(const gsl_rng * <var>r</var>, double <var>sigma</var>)</em></dt>
<dd><a name="index-Rayleigh-distribution"></a>
<p>This function returns a random variate from the Rayleigh distribution with
scale parameter <var>sigma</var>.  The distribution is,
</p>
<div class="example">
<pre class="example">p(x) dx = {x \over \sigma^2} \exp(- x^2/(2 \sigma^2)) dx
</pre></div>

<p>for <em>x &gt; 0</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fran_005frayleigh_005fpdf"></a>Function: <em>double</em> <strong>gsl_ran_rayleigh_pdf</strong> <em>(double <var>x</var>, double <var>sigma</var>)</em></dt>
<dd><p>This function computes the probability density <em>p(x)</em> at <var>x</var>
for a Rayleigh distribution with scale parameter <var>sigma</var>, using the
formula given above.
</p></dd></dl>

<br>

<dl>
<dt><a name="index-gsl_005fcdf_005frayleigh_005fP"></a>Function: <em>double</em> <strong>gsl_cdf_rayleigh_P</strong> <em>(double <var>x</var>, double <var>sigma</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005frayleigh_005fQ"></a>Function: <em>double</em> <strong>gsl_cdf_rayleigh_Q</strong> <em>(double <var>x</var>, double <var>sigma</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005frayleigh_005fPinv"></a>Function: <em>double</em> <strong>gsl_cdf_rayleigh_Pinv</strong> <em>(double <var>P</var>, double <var>sigma</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005frayleigh_005fQinv"></a>Function: <em>double</em> <strong>gsl_cdf_rayleigh_Qinv</strong> <em>(double <var>Q</var>, double <var>sigma</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 Rayleigh
distribution with scale parameter <var>sigma</var>.
</p></dd></dl>





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