This function returns a random variate from the Levy skew stable
distribution with scale c
, exponent alpha
and skewness
parameter beta
. The skewness parameter must lie in the range
[-1,1]. The Levy skew stable probability distribution is defined
by a Fourier transform,
\[p(x) = {1 \over 2 \pi} \int_{-\infty}^{+\infty}
\exp(-it x - |c t|^\alpha (1-i \beta \operatorname{sign}(t)
\tan(\pi \alpha/2))) dt\]
When \(\alpha = 1\) the term \(\tan(\pi \alpha/2)\) is replaced by
\(-(2/\pi)\log|t|\). There is no explicit solution for the form of
\(p(x)\) and the library does not define a corresponding pdf function.
For \(\alpha = 2\) the distribution reduces to a Gaussian distribution
with \(\sigma = \sqrt{2} c\) and the skewness parameter has no effect.
For \(\alpha < 1\) the tails of the distribution become extremely wide.
The symmetric distribution corresponds to \(\beta = 0\).
The algorithm only works for \(0 < \alpha \leq 2\).