Finite mixture of α-stable distributions

Over the last decades, the α-stable distribution has proved to be a very efficient model for impulsive data. In this paper, we propose an extension of stable distributions, namely mixture of α-stable distributions to model multimodal, skewed and impulsive data. A fully Bayesian framework is presented for the estimation of the stable density parameters and the mixture parameters. As opposed to most previous work on mixture models, the model order is assumed unknown and is estimated using reversible jump Markov chain Monte Carlo. It is important to note that the Gaussian mixture model is a special case of the presented model which provides additional flexibility to model skewed and impulsive phenomena. The algorithm is tested using synthetic and real data, accurately estimating α-stable parameters, mixture coefficients and the number of components in the mixture.