Approximation of α-stable probability densities using finite Gaussian mixtures

In this paper, we introduce a new analytical model for the a-stable probability density function (p.d.f). The new model is based on a corollary of the mixing theorem for symmetric α-stable (SαS) random variables (r.v.) [1] which states that a SαS r.v. can be expressed as the product of a Gaussian r.v. and a positive-stable r.v. We also extend this model to provide an analytical approximation for a subclass of multivariate a-stable p.d.f.s, namely the sub-Gaussian α-stable p.d.f.s. Simulation results indicate the success of our technique. The new analytical representation opens path to the application of maximum likelihood and Bayesian techniques for problems involving α-stable random variables. The paper is concluded with the examples of possible application areas.