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

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<a name="The-Cauchy-Distribution"></a>
<div class="header">
<p>
Next: <a href="The-Rayleigh-Distribution.html#The-Rayleigh-Distribution" accesskey="n" rel="next">The Rayleigh Distribution</a>, Previous: <a href="The-Exponential-Power-Distribution.html#The-Exponential-Power-Distribution" accesskey="p" rel="previous">The Exponential Power 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-Cauchy-Distribution-1"></a>
<h3 class="section">20.9 The Cauchy Distribution</h3>
<dl>
<dt><a name="index-gsl_005fran_005fcauchy"></a>Function: <em>double</em> <strong>gsl_ran_cauchy</strong> <em>(const gsl_rng * <var>r</var>, double <var>a</var>)</em></dt>
<dd><a name="index-Cauchy-distribution"></a>
<p>This function returns a random variate from the Cauchy distribution with
scale parameter <var>a</var>.  The probability distribution for Cauchy
random variates is,
</p>
<div class="example">
<pre class="example">p(x) dx = {1 \over a\pi (1 + (x/a)^2) } dx
</pre></div>

<p>for <em>x</em> in the range <em>-\infty</em> to <em>+\infty</em>.  The Cauchy
distribution is also known as the Lorentz distribution.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fran_005fcauchy_005fpdf"></a>Function: <em>double</em> <strong>gsl_ran_cauchy_pdf</strong> <em>(double <var>x</var>, double <var>a</var>)</em></dt>
<dd><p>This function computes the probability density <em>p(x)</em> at <var>x</var>
for a Cauchy distribution with scale parameter <var>a</var>, using the formula
given above.
</p></dd></dl>

<br>

<dl>
<dt><a name="index-gsl_005fcdf_005fcauchy_005fP"></a>Function: <em>double</em> <strong>gsl_cdf_cauchy_P</strong> <em>(double <var>x</var>, double <var>a</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fcauchy_005fQ"></a>Function: <em>double</em> <strong>gsl_cdf_cauchy_Q</strong> <em>(double <var>x</var>, double <var>a</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fcauchy_005fPinv"></a>Function: <em>double</em> <strong>gsl_cdf_cauchy_Pinv</strong> <em>(double <var>P</var>, double <var>a</var>)</em></dt>
<dt><a name="index-gsl_005fcdf_005fcauchy_005fQinv"></a>Function: <em>double</em> <strong>gsl_cdf_cauchy_Qinv</strong> <em>(double <var>Q</var>, double <var>a</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 Cauchy
distribution with scale parameter <var>a</var>.
</p></dd></dl>





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