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 \(0 < \alpha \leq 2\).