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<a name="The-Gamma-Distribution"></a>
<div class="header">
<p>
Next: <a href="The-Flat-_0028Uniform_0029-Distribution.html#The-Flat-_0028Uniform_0029-Distribution" accesskey="n" rel="next">The Flat (Uniform) Distribution</a>, Previous: <a href="The-Levy-skew-alpha_002dStable-Distribution.html#The-Levy-skew-alpha_002dStable-Distribution" accesskey="p" rel="previous">The Levy skew alpha-Stable Distribution</a>, Up: <a href="Random-Number-Distributions.html#Random-Number-Distributions" accesskey="u" rel="up">Random Number Distributions</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="The-Gamma-Distribution-1"></a>
<h3 class="section">20.15 The Gamma Distribution</h3>
<dl>
<dt><a name="index-gsl_005fran_005fgamma"></a>Function: <em>double</em> <strong>gsl_ran_gamma</strong> <em>(const gsl_rng * <var>r</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dd><a name="index-Gamma-distribution"></a>
<p>This function returns a random variate from the gamma
distribution. The distribution function is,
</p>
<div class="example">
<pre class="example">p(x) dx = {1 \over \Gamma(a) b^a} x^{a-1} e^{-x/b} dx
</pre></div>
<p>for <em>x > 0</em>.
</p>
<a name="index-Erlang-distribution"></a>
<p>The gamma distribution with an integer parameter <var>a</var> is known as the Erlang distribution.
</p>
<p>The variates are computed using the Marsaglia-Tsang fast gamma method.
This function for this method was previously called
<code>gsl_ran_gamma_mt</code> and can still be accessed using this name.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fran_005fgamma_005fknuth"></a>Function: <em>double</em> <strong>gsl_ran_gamma_knuth</strong> <em>(const gsl_rng * <var>r</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dd><p>This function returns a gamma variate using the algorithms from Knuth (vol 2).
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fran_005fgamma_005fpdf"></a>Function: <em>double</em> <strong>gsl_ran_gamma_pdf</strong> <em>(double <var>x</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dd><p>This function computes the probability density <em>p(x)</em> at <var>x</var>
for a gamma distribution with parameters <var>a</var> and <var>b</var>, using the
formula given above.
</p></dd></dl>
<br>
<dl>
<dt><a name="index-gsl_005fcdf_005fgamma_005fP"></a>Function: <em>double</em> <strong>gsl_cdf_gamma_P</strong> <em>(double <var>x</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fgamma_005fQ"></a>Function: <em>double</em> <strong>gsl_cdf_gamma_Q</strong> <em>(double <var>x</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fgamma_005fPinv"></a>Function: <em>double</em> <strong>gsl_cdf_gamma_Pinv</strong> <em>(double <var>P</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fgamma_005fQinv"></a>Function: <em>double</em> <strong>gsl_cdf_gamma_Qinv</strong> <em>(double <var>Q</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dd><p>These functions compute the cumulative distribution functions
<em>P(x)</em>, <em>Q(x)</em> and their inverses for the gamma
distribution with parameters <var>a</var> and <var>b</var>.
</p></dd></dl>
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