Modelling with mixture of symmetric stable distributions using Gibbs sampling

The stable distribution is a very useful tool to model impulsive data. In this work, a fully Bayesian mixture of symmetric stable distribution model is presented. Despite the non-existence of closed form for alpha-stable distributions, the use of the product property makes it possible to infer on parameters using a straight forward Gibbs sampling. This model is compared to the mixture of Gaussians model. Our proposed methodology is proved to be more robust to outliers than the mixture of Gaussians. Therefore, it is suitable to model mixture of impulsive data. Moreover, as Gaussian is a particular case of the alpha-stable distribution, the proposed model is a generalization of mixture of Gaussians. Mixture of symmetric alpha-stable is intensively tested on both simulated and real data.