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

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<a name="The-Poisson-Distribution"></a>
<div class="header">
<p>
Next: <a href="The-Bernoulli-Distribution.html#The-Bernoulli-Distribution" accesskey="n" rel="next">The Bernoulli Distribution</a>, Previous: <a href="General-Discrete-Distributions.html#General-Discrete-Distributions" accesskey="p" rel="previous">General Discrete Distributions</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-Poisson-Distribution-1"></a>
<h3 class="section">20.30 The Poisson Distribution</h3>
<dl>
<dt><a name="index-gsl_005fran_005fpoisson"></a>Function: <em>unsigned int</em> <strong>gsl_ran_poisson</strong> <em>(const gsl_rng * <var>r</var>, double <var>mu</var>)</em></dt>
<dd><a name="index-Poisson-random-numbers"></a>
<p>This function returns a random integer from the Poisson distribution
with mean <var>mu</var>.  The probability distribution for Poisson variates is,
</p>
<div class="example">
<pre class="example">p(k) = {\mu^k \over k!} \exp(-\mu)
</pre></div>

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

<dl>
<dt><a name="index-gsl_005fran_005fpoisson_005fpdf"></a>Function: <em>double</em> <strong>gsl_ran_poisson_pdf</strong> <em>(unsigned int <var>k</var>, double <var>mu</var>)</em></dt>
<dd><p>This function computes the probability <em>p(k)</em> of obtaining  <var>k</var>
from a Poisson distribution with mean <var>mu</var>, using the formula
given above.
</p></dd></dl>

<br>

<dl>
<dt><a name="index-gsl_005fcdf_005fpoisson_005fP"></a>Function: <em>double</em> <strong>gsl_cdf_poisson_P</strong> <em>(unsigned int <var>k</var>, double <var>mu</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fpoisson_005fQ"></a>Function: <em>double</em> <strong>gsl_cdf_poisson_Q</strong> <em>(unsigned int <var>k</var>, double <var>mu</var>)</em></dt>
<dd><p>These functions compute the cumulative distribution functions
<em>P(k)</em>, <em>Q(k)</em> for the Poisson distribution with parameter
<var>mu</var>.
</p></dd></dl>





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