# The Cauchy Distribution¶

gsl_ran_cauchy(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.

gsl_ran_cauchy_pdf(x, a)

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

gsl_ran_cauchy_P(x, a)
gsl_ran_cauchy_Q(x, a)
gsl_ran_cauchy_Pinv(P, a)
gsl_ran_cauchy_Qinv(Q, a)

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