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<title>The Cauchy Distribution - GNU Scientific Library -- Reference Manual</title>
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<a name="The-Cauchy-Distribution"></a>
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<h3 class="section">20.8 The Cauchy Distribution</h3>
<div class="defun">
— Function: double <b>gsl_ran_cauchy</b> (<var>const gsl_rng * r, double a</var>)<var><a name="index-gsl_005fran_005fcauchy-1725"></a></var><br>
<blockquote><p><a name="index-Cauchy-distribution-1726"></a>This function returns a random variate from the Cauchy distribution with
scale parameter <var>a</var>. The probability distribution for Cauchy
random variates is,
<pre class="example"> p(x) dx = {1 \over a\pi (1 + (x/a)^2) } dx
</pre>
<p class="noindent">for x in the range -\infty to +\infty. The Cauchy
distribution is also known as the Lorentz distribution.
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_ran_cauchy_pdf</b> (<var>double x, double a</var>)<var><a name="index-gsl_005fran_005fcauchy_005fpdf-1727"></a></var><br>
<blockquote><p>This function computes the probability density p(x) at <var>x</var>
for a Cauchy distribution with scale parameter <var>a</var>, using the formula
given above.
</p></blockquote></div>
<pre class="sp">
</pre>
<div class="defun">
— Function: double <b>gsl_cdf_cauchy_P</b> (<var>double x, double a</var>)<var><a name="index-gsl_005fcdf_005fcauchy_005fP-1728"></a></var><br>
— Function: double <b>gsl_cdf_cauchy_Q</b> (<var>double x, double a</var>)<var><a name="index-gsl_005fcdf_005fcauchy_005fQ-1729"></a></var><br>
— Function: double <b>gsl_cdf_cauchy_Pinv</b> (<var>double P, double a</var>)<var><a name="index-gsl_005fcdf_005fcauchy_005fPinv-1730"></a></var><br>
— Function: double <b>gsl_cdf_cauchy_Qinv</b> (<var>double Q, double a</var>)<var><a name="index-gsl_005fcdf_005fcauchy_005fQinv-1731"></a></var><br>
<blockquote><p>These functions compute the cumulative distribution functions
P(x), Q(x) and their inverses for the Cauchy
distribution with scale parameter <var>a</var>.
</p></blockquote></div>
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