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<title>The Type-1 Gumbel Distribution - GNU Scientific Library -- Reference Manual</title>
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<h3 class="section">19.25 The Type-1 Gumbel Distribution</h3>
<div class="defun">
— Function: double <b>gsl_ran_gumbel1</b> (<var>const gsl_rng * r, double a, double b</var>)<var><a name="index-gsl_005fran_005fgumbel1-1736"></a></var><br>
<blockquote><p><a name="index-Gumbel-distribution-_0028Type-1_0029-1737"></a><a name="index-Type-1-Gumbel-distribution_002c-random-variates-1738"></a>This function returns a random variate from the Type-1 Gumbel
distribution. The Type-1 Gumbel distribution function is,
<pre class="example"> p(x) dx = a b \exp(-(b \exp(-ax) + ax)) dx
</pre>
<p class="noindent">for -\infty < x < \infty.
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_ran_gumbel1_pdf</b> (<var>double x, double a, double b</var>)<var><a name="index-gsl_005fran_005fgumbel1_005fpdf-1739"></a></var><br>
<blockquote><p>This function computes the probability density p(x) 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></blockquote></div>
<pre class="sp">
</pre>
<div class="defun">
— Function: double <b>gsl_cdf_gumbel1_P</b> (<var>double x, double a, double b</var>)<var><a name="index-gsl_005fcdf_005fgumbel1_005fP-1740"></a></var><br>
— Function: double <b>gsl_cdf_gumbel1_Q</b> (<var>double x, double a, double b</var>)<var><a name="index-gsl_005fcdf_005fgumbel1_005fQ-1741"></a></var><br>
— Function: double <b>gsl_cdf_gumbel1_Pinv</b> (<var>double P, double a, double b</var>)<var><a name="index-gsl_005fcdf_005fgumbel1_005fPinv-1742"></a></var><br>
— Function: double <b>gsl_cdf_gumbel1_Qinv</b> (<var>double Q, double a, double b</var>)<var><a name="index-gsl_005fcdf_005fgumbel1_005fQinv-1743"></a></var><br>
<blockquote><p>These functions compute the cumulative distribution functions
P(x), Q(x) and their inverses for the Type-1 Gumbel
distribution with parameters <var>a</var> and <var>b</var>.
</p></blockquote></div>
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