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