Three-Component Mixture Approximation for Standard Symmetric Alpha-Stable Distribution

In this paper, a new three-component mixture for approximation of probability density function (PDF) of alpha-stable distribution is investigated. Closed-form expression for PDF is a serious consideration in signal processing. However, alpha-stable distribution has no closed-form expression for PDF. Heretofore several models try to propose a mixture model for approximation of this PDF. Here, we have a new mixture approximation by means of three distributions with closed-form PDF such as Cauchy, Gaussian and Holtsmark distributions for symmetric alpha-stable PDF with known parameters. The results of the simulations indicate that this mixture shows a significant improvement over previous mixtures.