Statistical Inference for Mixture of Cauchy Distributions

The class of $\alpha$-stable distributions received much interest for modelling impulsive phenomena occur in engineering, economics, insurance, and physics. The lack of non-analytical form for probability density function is considered as the main obstacle to modelling data via the class of $\alpha$-stable distributions. As the central member of this class, the Cauchy distribution has received many applications in economics, seismology, theoretical and applied physics. We derive estimators for the parameters of the Cauchy and mixture of Cauchy distributions through the EM algorithm. Performance of the EM algorithm is demonstrated through simulations and real sets of data.