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<title>GNU Scientific Library &ndash; Reference Manual: The Type-1 Gumbel Distribution</title>

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<a name="The-Type_002d1-Gumbel-Distribution"></a>
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<p>
Next: <a href="The-Type_002d2-Gumbel-Distribution.html#The-Type_002d2-Gumbel-Distribution" accesskey="n" rel="next">The Type-2 Gumbel Distribution</a>, Previous: <a href="The-Weibull-Distribution.html#The-Weibull-Distribution" accesskey="p" rel="previous">The Weibull 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-Type_002d1-Gumbel-Distribution-1"></a>
<h3 class="section">20.26 The Type-1 Gumbel Distribution</h3>
<dl>
<dt><a name="index-gsl_005fran_005fgumbel1"></a>Function: <em>double</em> <strong>gsl_ran_gumbel1</strong> <em>(const gsl_rng * <var>r</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dd><a name="index-Gumbel-distribution-_0028Type-1_0029"></a>
<a name="index-Type-1-Gumbel-distribution_002c-random-variates"></a>
<p>This function returns  a random variate from the Type-1 Gumbel
distribution.  The Type-1 Gumbel distribution function is,
</p>
<div class="example">
<pre class="example">p(x) dx = a b \exp(-(b \exp(-ax) + ax)) dx
</pre></div>

<p>for <em>-\infty &lt; x &lt; \infty</em>. 
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fran_005fgumbel1_005fpdf"></a>Function: <em>double</em> <strong>gsl_ran_gumbel1_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 Type-1 Gumbel 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_005fgumbel1_005fP"></a>Function: <em>double</em> <strong>gsl_cdf_gumbel1_P</strong> <em>(double <var>x</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fgumbel1_005fQ"></a>Function: <em>double</em> <strong>gsl_cdf_gumbel1_Q</strong> <em>(double <var>x</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fgumbel1_005fPinv"></a>Function: <em>double</em> <strong>gsl_cdf_gumbel1_Pinv</strong> <em>(double <var>P</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fgumbel1_005fQinv"></a>Function: <em>double</em> <strong>gsl_cdf_gumbel1_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 Type-1 Gumbel
distribution with parameters <var>a</var> and <var>b</var>.
</p></dd></dl>





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