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

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<a name="The-Weibull-Distribution"></a>
<div class="header">
<p>
Next: <a href="The-Type_002d1-Gumbel-Distribution.html#The-Type_002d1-Gumbel-Distribution" accesskey="n" rel="next">The Type-1 Gumbel Distribution</a>, Previous: <a href="Spherical-Vector-Distributions.html#Spherical-Vector-Distributions" accesskey="p" rel="previous">Spherical Vector Distributions</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>
</div>
<hr>
<a name="The-Weibull-Distribution-1"></a>
<h3 class="section">20.25 The Weibull Distribution</h3>
<dl>
<dt><a name="index-gsl_005fran_005fweibull"></a>Function: <em>double</em> <strong>gsl_ran_weibull</strong> <em>(const gsl_rng * <var>r</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dd><a name="index-Weibull-distribution"></a>
<p>This function returns a random variate from the Weibull distribution.  The
distribution function is,
</p>
<div class="example">
<pre class="example">p(x) dx = {b \over a^b} x^{b-1}  \exp(-(x/a)^b) dx
</pre></div>

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

<dl>
<dt><a name="index-gsl_005fran_005fweibull_005fpdf"></a>Function: <em>double</em> <strong>gsl_ran_weibull_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 Weibull distribution with scale <var>a</var> and exponent <var>b</var>,
using the formula given above.
</p></dd></dl>

<br>

<dl>
<dt><a name="index-gsl_005fcdf_005fweibull_005fP"></a>Function: <em>double</em> <strong>gsl_cdf_weibull_P</strong> <em>(double <var>x</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fweibull_005fQ"></a>Function: <em>double</em> <strong>gsl_cdf_weibull_Q</strong> <em>(double <var>x</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fweibull_005fPinv"></a>Function: <em>double</em> <strong>gsl_cdf_weibull_Pinv</strong> <em>(double <var>P</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fweibull_005fQinv"></a>Function: <em>double</em> <strong>gsl_cdf_weibull_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 Weibull
distribution with scale <var>a</var> and exponent <var>b</var>.
</p></dd></dl>





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