A poisson series approach to Bayesian Monte Carlo inference for skewed alpha-stable distributions

In this paper we study parameter estimation for α-stable distribution parameters. The proposed approach uses a Poisson series representation (PSR) for skewed α-stable random variables, which provides a conditionally Gaussian framework. Therefore, a straightforward implementation of Bayesian parameter estimation using Markov chain Monte Carlo (MCMC) methods is feasible. To extend the series representation to practical application, we provide a novel approximation of the series residual terms, which exactly characterises the mean and variance of the approximation and maintains its structure. Simulations illustrate the proposed framework applied to skewed α-stable data, estimating the distribution parameter values.