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<a name="The-Geometric-Distribution"></a>
<div class="header">
<p>
Next: <a href="The-Hypergeometric-Distribution.html#The-Hypergeometric-Distribution" accesskey="n" rel="next">The Hypergeometric Distribution</a>, Previous: <a href="The-Pascal-Distribution.html#The-Pascal-Distribution" accesskey="p" rel="previous">The Pascal 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-Geometric-Distribution-1"></a>
<h3 class="section">20.36 The Geometric Distribution</h3>
<dl>
<dt><a name="index-gsl_005fran_005fgeometric"></a>Function: <em>unsigned int</em> <strong>gsl_ran_geometric</strong> <em>(const gsl_rng * <var>r</var>, double <var>p</var>)</em></dt>
<dd><a name="index-Geometric-random-variates"></a>
<p>This function returns a random integer from the geometric distribution,
the number of independent trials with probability <var>p</var> until the
first success.  The probability distribution for geometric variates
is,
</p>
<div class="example">
<pre class="example">p(k) =  p (1-p)^(k-1)
</pre></div>

<p>for <em>k &gt;= 1</em>.  Note that the distribution begins with <em>k=1</em> with this
definition.  There is another convention in which the exponent <em>k-1</em> 
is replaced by <em>k</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fran_005fgeometric_005fpdf"></a>Function: <em>double</em> <strong>gsl_ran_geometric_pdf</strong> <em>(unsigned int <var>k</var>, double <var>p</var>)</em></dt>
<dd><p>This function computes the probability <em>p(k)</em> of obtaining <var>k</var>
from a geometric distribution with probability parameter <var>p</var>, using
the formula given above.
</p></dd></dl>

<br>

<dl>
<dt><a name="index-gsl_005fcdf_005fgeometric_005fP"></a>Function: <em>double</em> <strong>gsl_cdf_geometric_P</strong> <em>(unsigned int <var>k</var>, double <var>p</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fgeometric_005fQ"></a>Function: <em>double</em> <strong>gsl_cdf_geometric_Q</strong> <em>(unsigned int <var>k</var>, double <var>p</var>)</em></dt>
<dd><p>These functions compute the cumulative distribution functions
<em>P(k)</em>, <em>Q(k)</em> for the geometric distribution with parameter
<var>p</var>.
</p></dd></dl>





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