### 20.8 The Cauchy Distribution

— Function: double gsl_ran_cauchy (const gsl_rng * r, double a)

This function returns a random variate from the Cauchy distribution with scale parameter a. The probability distribution for Cauchy random variates is,

          p(x) dx = {1 \over a\pi (1 + (x/a)^2) } dx


for x in the range -\infty to +\infty. The Cauchy distribution is also known as the Lorentz distribution.

— Function: double gsl_ran_cauchy_pdf (double x, double a)

This function computes the probability density p(x) at x for a Cauchy distribution with scale parameter a, using the formula given above.



— Function: double gsl_cdf_cauchy_P (double x, double a)
— Function: double gsl_cdf_cauchy_Q (double x, double a)
— Function: double gsl_cdf_cauchy_Pinv (double P, double a)
— Function: double gsl_cdf_cauchy_Qinv (double Q, double a)

These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Cauchy distribution with scale parameter a.

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