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<a name="The-Landau-Distribution"></a>
<div class="header">
<p>
Next: <a href="The-Levy-alpha_002dStable-Distributions.html#The-Levy-alpha_002dStable-Distributions" accesskey="n" rel="next">The Levy alpha-Stable Distributions</a>, Previous: <a href="The-Rayleigh-Tail-Distribution.html#The-Rayleigh-Tail-Distribution" accesskey="p" rel="previous">The Rayleigh Tail 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-Landau-Distribution-1"></a>
<h3 class="section">20.12 The Landau Distribution</h3>
<dl>
<dt><a name="index-gsl_005fran_005flandau"></a>Function: <em>double</em> <strong>gsl_ran_landau</strong> <em>(const gsl_rng * <var>r</var>)</em></dt>
<dd><a name="index-Landau-distribution"></a>
<p>This function returns a random variate from the Landau distribution.  The
probability distribution for Landau random variates is defined
analytically by the complex integral,
</p>
<div class="example">
<pre class="example">p(x) = (1/(2 \pi i)) \int_{c-i\infty}^{c+i\infty} ds exp(s log(s) + x s) 
</pre></div>
<p>For numerical purposes it is more convenient to use the following
equivalent form of the integral,
</p>
<div class="example">
<pre class="example">p(x) = (1/\pi) \int_0^\infty dt \exp(-t \log(t) - x t) \sin(\pi t).
</pre></div>
</dd></dl>

<dl>
<dt><a name="index-gsl_005fran_005flandau_005fpdf"></a>Function: <em>double</em> <strong>gsl_ran_landau_pdf</strong> <em>(double <var>x</var>)</em></dt>
<dd><p>This function computes the probability density <em>p(x)</em> at <var>x</var>
for the Landau distribution using an approximation to the formula given
above.
</p></dd></dl>

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