Bayesian estimation of mixtures of skewed alpha stable distributions with an unknown number of components

Alpha stable distributions are widely accepted models for impulsive data. Despite their flexibility in modelling varying degrees of impulsiveness and skewness, they fall short of modelling multimodal data. In this work, we present the alpha-stable mixture model which provides a framework for modelling multimodal, skewed and impulsive data. We describe new parameter estimation techniques for this model based on numerical Bayesian techniques which not only can estimate the alpha-stable and mixture parameters, but also the number of components in the mixture. In particular, we employ the reversible jump Markov chain Monte Carlo technique.