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- Function:
*double***gsl_ran_levy_skew***(const gsl_rng **`r`, double`c`, double`alpha`, double`beta`) -
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} dt \exp(-it x - |c t|^alpha (1-i beta sign(t) tan(pi alpha/2)))

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 <= 2*.

The Levy alpha-stable distributions have the property that if *N*
alpha-stable variates are drawn from the distribution *p(c, \alpha,
\beta)* then the sum *Y = X_1 + X_2 + \dots + X_N* will also be
distributed as an alpha-stable variate,
*p(N^(1/\alpha) c, \alpha, \beta)*.