Parameter Estimation Using the EM Algorithm for Symmetric Stable Random Variables and Sub-Gaussian Random Vectors

Abstract

Applying some well-known properties of the class of symmetric α-stable (SαS) distribution, the EM algorithm is extended to estimate the parameters of SαS distributions. Furthermore, we extend this algorithm to the multivariate sub-Gaussian α-stable distributions. Some comparative studies are performed through simulation and for some real data sets to show the performance of the proposed EM algorithm compared with some well-known methods including empirical characteristic function, maximum likelihood, and sample quantile in the univariate and multivariate cases.

Keywords

• EM algorithm
• Markov Chain Monte Carlo
• Symmetric α-stable distribution (SαS)
• Sub-Gaussian α-stable distribution