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.

The Exponential Power Distribution

The Rayleigh Distribution