A Study of Skewed Heavy-Tailed Distributions as Scale Mixtures

Abstract

SYNOPTIC ABSTRACTIn this article, we study and compare different proposals of heavy-tailed (possibly skewed) distributions as robust alternatives to the normal model. The density functions are all represented as scale mixtures, which enables efficient Bayesian estimation via Markov chain Monte Carlo (MCMC) methods. However, although the symmetric versions of these distributions are able to model heavy tails, they of course fail to capture asymmetry; for example, when the dataset contains extreme values in one of the tails. Therefore, distributions that accommodate skewness, as well as fat tails, are taken into account.