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<a name="The-Hypergeometric-Distribution"></a>
<div class="header">
<p>
Next: <a href="The-Logarithmic-Distribution.html#The-Logarithmic-Distribution" accesskey="n" rel="next">The Logarithmic Distribution</a>, Previous: <a href="The-Geometric-Distribution.html#The-Geometric-Distribution" accesskey="p" rel="previous">The Geometric 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-Hypergeometric-Distribution-1"></a>
<h3 class="section">20.37 The Hypergeometric Distribution</h3>
<a name="index-hypergeometric-random-variates"></a>
<dl>
<dt><a name="index-gsl_005fran_005fhypergeometric"></a>Function: <em>unsigned int</em> <strong>gsl_ran_hypergeometric</strong> <em>(const gsl_rng * <var>r</var>, unsigned int <var>n1</var>, unsigned int <var>n2</var>, unsigned int <var>t</var>)</em></dt>
<dd><a name="index-Geometric-random-variates-1"></a>
<p>This function returns a random integer from the hypergeometric
distribution.  The probability distribution for hypergeometric
random variates is,
</p>
<div class="example">
<pre class="example">p(k) =  C(n_1, k) C(n_2, t - k) / C(n_1 + n_2, t)
</pre></div>

<p>where <em>C(a,b) = a!/(b!(a-b)!)</em> and 
<em>t &lt;= n_1 + n_2</em>.  The domain of <em>k</em> is 
<em>max(0,t-n_2), ..., min(t,n_1)</em>.
</p>
<p>If a population contains <em>n_1</em> elements of &ldquo;type 1&rdquo; and
<em>n_2</em> elements of &ldquo;type 2&rdquo; then the hypergeometric
distribution gives the probability of obtaining <em>k</em> elements of
&ldquo;type 1&rdquo; in <em>t</em> samples from the population without
replacement.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fran_005fhypergeometric_005fpdf"></a>Function: <em>double</em> <strong>gsl_ran_hypergeometric_pdf</strong> <em>(unsigned int <var>k</var>, unsigned int <var>n1</var>, unsigned int <var>n2</var>, unsigned int <var>t</var>)</em></dt>
<dd><p>This function computes the probability <em>p(k)</em> of obtaining <var>k</var>
from a hypergeometric distribution with parameters <var>n1</var>, <var>n2</var>,
<var>t</var>, using the formula given above.
</p></dd></dl>

<br>

<dl>
<dt><a name="index-gsl_005fcdf_005fhypergeometric_005fP"></a>Function: <em>double</em> <strong>gsl_cdf_hypergeometric_P</strong> <em>(unsigned int <var>k</var>, unsigned int <var>n1</var>, unsigned int <var>n2</var>, unsigned int <var>t</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fhypergeometric_005fQ"></a>Function: <em>double</em> <strong>gsl_cdf_hypergeometric_Q</strong> <em>(unsigned int <var>k</var>, unsigned int <var>n1</var>, unsigned int <var>n2</var>, unsigned int <var>t</var>)</em></dt>
<dd><p>These functions compute the cumulative distribution functions
<em>P(k)</em>, <em>Q(k)</em> for the hypergeometric distribution with
parameters <var>n1</var>, <var>n2</var> and <var>t</var>.
</p></dd></dl>





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