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<title>The Hypergeometric Distribution - GNU Scientific Library -- Reference Manual</title>
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<p>
<a name="The-Hypergeometric-Distribution"></a>
Next: <a rel="next" accesskey="n" href="The-Logarithmic-Distribution.html">The Logarithmic Distribution</a>,
Previous: <a rel="previous" accesskey="p" href="The-Geometric-Distribution.html">The Geometric Distribution</a>,
Up: <a rel="up" accesskey="u" href="Random-Number-Distributions.html">Random Number Distributions</a>
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<h3 class="section">20.36 The Hypergeometric Distribution</h3>
<p><a name="index-hypergeometric-random-variates-1898"></a>
<div class="defun">
— Function: unsigned int <b>gsl_ran_hypergeometric</b> (<var>const gsl_rng * r, unsigned int n1, unsigned int n2, unsigned int t</var>)<var><a name="index-gsl_005fran_005fhypergeometric-1899"></a></var><br>
<blockquote><p><a name="index-Geometric-random-variates-1900"></a>This function returns a random integer from the hypergeometric
distribution. The probability distribution for hypergeometric
random variates is,
<pre class="example"> p(k) = C(n_1, k) C(n_2, t - k) / C(n_1 + n_2, t)
</pre>
<p class="noindent">where C(a,b) = a!/(b!(a-b)!) and
<!-- {$t \leq n_1 + n_2$} -->
t <= n_1 + n_2. The domain of k is
<!-- {$\hbox{max}(0,t-n_2), \ldots, \hbox{min}(t,n_1)$} -->
max(0,t-n_2), ..., min(t,n_1).
<p>If a population contains n_1 elements of “type 1” and
n_2 elements of “type 2” then the hypergeometric
distribution gives the probability of obtaining k elements of
“type 1” in t samples from the population without
replacement.
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_ran_hypergeometric_pdf</b> (<var>unsigned int k, unsigned int n1, unsigned int n2, unsigned int t</var>)<var><a name="index-gsl_005fran_005fhypergeometric_005fpdf-1901"></a></var><br>
<blockquote><p>This function computes the probability p(k) 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></blockquote></div>
<pre class="sp">
</pre>
<div class="defun">
— Function: double <b>gsl_cdf_hypergeometric_P</b> (<var>unsigned int k, unsigned int n1, unsigned int n2, unsigned int t</var>)<var><a name="index-gsl_005fcdf_005fhypergeometric_005fP-1902"></a></var><br>
— Function: double <b>gsl_cdf_hypergeometric_Q</b> (<var>unsigned int k, unsigned int n1, unsigned int n2, unsigned int t</var>)<var><a name="index-gsl_005fcdf_005fhypergeometric_005fQ-1903"></a></var><br>
<blockquote><p>These functions compute the cumulative distribution functions
P(k), Q(k) for the hypergeometric distribution with
parameters <var>n1</var>, <var>n2</var> and <var>t</var>.
</p></blockquote></div>
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