20.9 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.