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

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<a name="The-Negative-Binomial-Distribution"></a>
<div class="header">
<p>
Next: <a href="The-Pascal-Distribution.html#The-Pascal-Distribution" accesskey="n" rel="next">The Pascal Distribution</a>, Previous: <a href="The-Multinomial-Distribution.html#The-Multinomial-Distribution" accesskey="p" rel="previous">The Multinomial 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-Negative-Binomial-Distribution-1"></a>
<h3 class="section">20.34 The Negative Binomial Distribution</h3>
<dl>
<dt><a name="index-gsl_005fran_005fnegative_005fbinomial"></a>Function: <em>unsigned int</em> <strong>gsl_ran_negative_binomial</strong> <em>(const gsl_rng * <var>r</var>, double <var>p</var>, double <var>n</var>)</em></dt>
<dd><a name="index-Negative-Binomial-distribution_002c-random-variates"></a>
<p>This function returns a random integer from the negative binomial
distribution, the number of failures occurring before <var>n</var> successes
in independent trials with probability <var>p</var> of success.  The
probability distribution for negative binomial variates is,
</p>
<div class="example">
<pre class="example">p(k) = {\Gamma(n + k) \over \Gamma(k+1) \Gamma(n) } p^n (1-p)^k
</pre></div>

<p>Note that <em>n</em> is not required to be an integer.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fran_005fnegative_005fbinomial_005fpdf"></a>Function: <em>double</em> <strong>gsl_ran_negative_binomial_pdf</strong> <em>(unsigned int <var>k</var>, double <var>p</var>, double  <var>n</var>)</em></dt>
<dd><p>This function computes the probability <em>p(k)</em> of obtaining <var>k</var>
from a negative binomial distribution with parameters <var>p</var> and
<var>n</var>, using the formula given above.
</p></dd></dl>

<br>

<dl>
<dt><a name="index-gsl_005fcdf_005fnegative_005fbinomial_005fP"></a>Function: <em>double</em> <strong>gsl_cdf_negative_binomial_P</strong> <em>(unsigned int <var>k</var>, double <var>p</var>, double <var>n</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fnegative_005fbinomial_005fQ"></a>Function: <em>double</em> <strong>gsl_cdf_negative_binomial_Q</strong> <em>(unsigned int <var>k</var>, double <var>p</var>, double <var>n</var>)</em></dt>
<dd><p>These functions compute the cumulative distribution functions
<em>P(k)</em>, <em>Q(k)</em> for the negative binomial distribution with
parameters <var>p</var> and <var>n</var>.
</p></dd></dl>




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