The Levy alpha-Stable Distributions

Random: double gsl_ran_levy (const gsl_rng * r, double c, double alpha)

This function returns a random variate from the Levy symmetric stable distribution with scale c and exponent alpha. The symmetric stable probability distribution is defined by a fourier transform,

There is no explicit solution for the form of @math{p(x)} and the library does not define a corresponding pdf function. For @math{\alpha = 1} the distribution reduces to the Cauchy distribution. For @math{\alpha = 2} it is a Gaussian distribution with @c{$\sigma = \sqrt{2} c$} @math{\sigma = \sqrt{2} c}. For @math{\alpha < 1} the tails of the distribution become extremely wide.

The algorithm only works for @c{$0 < \alpha \le 2$} @math{0 < alpha <= 2}.