Expectation maximization (EM) algorithm and the Bayesian techniques are two approaches for statistical inference of mixture models [3, 4]. By noting the advantages of the Bayesian methods, practitioners prefer them. However, implementing Markov chain Monte Carlo algorithms can be very complicated for stable distributions, due to the non‐analytic density or distribution function formulas.
In this paper, we introduce a new class of mixture of heavy‐tailed distributions, called mixture of skewed stable distributions. Skewed stable distributions belongs to the exponential family and they have analytic density representation. It is shown that skewed stable distributions dominate skew stable distribution functions and they can be used to model heavy‐tailed data.
The class of skewed stable distributions has an analytic representation for its density function and the Bayesian inference can be done similar to the exponential family of distributions.
Finally, mixture of skewed stable distributions are compared to the mixture of stable distributions through a simulations study.