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

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<a name="The-Pascal-Distribution"></a>
<div class="header">
<p>
Next: <a href="The-Geometric-Distribution.html#The-Geometric-Distribution" accesskey="n" rel="next">The Geometric Distribution</a>, Previous: <a href="The-Negative-Binomial-Distribution.html#The-Negative-Binomial-Distribution" accesskey="p" rel="previous">The Negative Binomial 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-Pascal-Distribution-1"></a>
<h3 class="section">20.35 The Pascal Distribution</h3>

<dl>
<dt><a name="index-gsl_005fran_005fpascal"></a>Function: <em>unsigned int</em> <strong>gsl_ran_pascal</strong> <em>(const gsl_rng * <var>r</var>, double <var>p</var>, unsigned int <var>n</var>)</em></dt>
<dd><p>This function returns a random integer from the Pascal distribution.  The
Pascal distribution is simply a negative binomial distribution with an
integer value of <em>n</em>.
</p>
<div class="example">
<pre class="example">p(k) = {(n + k - 1)! \over k! (n - 1)! } p^n (1-p)^k
</pre></div>

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

<dl>
<dt><a name="index-gsl_005fran_005fpascal_005fpdf"></a>Function: <em>double</em> <strong>gsl_ran_pascal_pdf</strong> <em>(unsigned int <var>k</var>, double <var>p</var>, unsigned int <var>n</var>)</em></dt>
<dd><p>This function computes the probability <em>p(k)</em> of obtaining <var>k</var>
from a Pascal 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_005fpascal_005fP"></a>Function: <em>double</em> <strong>gsl_cdf_pascal_P</strong> <em>(unsigned int <var>k</var>, double <var>p</var>, unsigned int <var>n</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fpascal_005fQ"></a>Function: <em>double</em> <strong>gsl_cdf_pascal_Q</strong> <em>(unsigned int <var>k</var>, double <var>p</var>, unsigned int <var>n</var>)</em></dt>
<dd><p>These functions compute the cumulative distribution functions
<em>P(k)</em>, <em>Q(k)</em> for the Pascal distribution with
parameters <var>p</var> and <var>n</var>.
</p></dd></dl>




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