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<a name="The-Exponential-Power-Distribution"></a>
<div class="header">
<p>
Next: <a href="The-Cauchy-Distribution.html#The-Cauchy-Distribution" accesskey="n" rel="next">The Cauchy Distribution</a>, Previous: <a href="The-Laplace-Distribution.html#The-Laplace-Distribution" accesskey="p" rel="previous">The Laplace 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>
</div>
<hr>
<a name="The-Exponential-Power-Distribution-1"></a>
<h3 class="section">20.8 The Exponential Power Distribution</h3>
<dl>
<dt><a name="index-gsl_005fran_005fexppow"></a>Function: <em>double</em> <strong>gsl_ran_exppow</strong> <em>(const gsl_rng * <var>r</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dd><a name="index-Exponential-power-distribution"></a>
<p>This function returns a random variate from the exponential power distribution
with scale parameter <var>a</var> and exponent <var>b</var>.  The distribution is,
</p>
<div class="example">
<pre class="example">p(x) dx = {1 \over 2 a \Gamma(1+1/b)} \exp(-|x/a|^b) dx
</pre></div>

<p>for <em>x &gt;= 0</em>.  For <em>b = 1</em> this reduces to the Laplace
distribution.  For <em>b = 2</em> it has the same form as a Gaussian
distribution, but with <em>a = \sqrt{2} \sigma</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fran_005fexppow_005fpdf"></a>Function: <em>double</em> <strong>gsl_ran_exppow_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 an exponential power distribution with scale parameter <var>a</var>
and exponent <var>b</var>, using the formula given above.
</p></dd></dl>

<br>

<dl>
<dt><a name="index-gsl_005fcdf_005fexppow_005fP"></a>Function: <em>double</em> <strong>gsl_cdf_exppow_P</strong> <em>(double <var>x</var>, double <var>a</var>, double <var>b</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fexppow_005fQ"></a>Function: <em>double</em> <strong>gsl_cdf_exppow_Q</strong> <em>(double <var>x</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> for the exponential power distribution with
parameters <var>a</var> and <var>b</var>.
</p></dd></dl>





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