


The Levy alpha-Stable Distribution
==================================

.. function:: gsl_ran_levy(c, alpha)

 This function returns a random variate from the :index:`Levy symmetric
 stable distribution` with scale ``c`` and exponent ``alpha``.
 The symmetric stable probability distribution is defined by a
 Fourier transform,

 .. math::
   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 :math:`p(x)` and the library
 does not define a corresponding pdf function. For :math:`\alpha = 1` the
 distribution reduces to the Cauchy distribution. For :math:`\alpha = 2` it
 is a Gaussian distribution with :math:`\sigma = \sqrt{2} c`. For :math:`\alpha < 1`
 the tails of the distribution become extremely wide.

 The algorithm only works for :math:`0 < \alpha \leq 2`.
