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<title>The Landau Distribution - GNU Scientific Library -- Reference Manual</title>
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<a name="The-Landau-Distribution"></a>
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<h3 class="section">19.11 The Landau Distribution</h3>
<div class="defun">
— Function: double <b>gsl_ran_landau</b> (<var>const gsl_rng * r</var>)<var><a name="index-gsl_005fran_005flandau-1641"></a></var><br>
<blockquote><p><a name="index-Landau-distribution-1642"></a>This function returns a random variate from the Landau distribution. The
probability distribution for Landau random variates is defined
analytically by the complex integral,
<pre class="example"> p(x) = (1/(2 \pi i)) \int_{c-i\infty}^{c+i\infty} ds exp(s log(s) + x s)
</pre>
<p>For numerical purposes it is more convenient to use the following
equivalent form of the integral,
<pre class="example"> p(x) = (1/\pi) \int_0^\infty dt \exp(-t \log(t) - x t) \sin(\pi t).
</pre>
</blockquote></div>
<div class="defun">
— Function: double <b>gsl_ran_landau_pdf</b> (<var>double x</var>)<var><a name="index-gsl_005fran_005flandau_005fpdf-1643"></a></var><br>
<blockquote><p>This function computes the probability density p(x) at <var>x</var>
for the Landau distribution using an approximation to the formula given
above.
</p></blockquote></div>
<pre class="sp">
</pre>
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