# The Levy alpha-Stable Distribution¶

gsl_ran_levy(c, 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,

$p(x) = {1 \over 2 \pi} \int_{-\infty}^{+\infty} \exp(-it x - |c t|^\alpha) dt$

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

The algorithm only works for $$0 < \alpha \leq 2$$.