A Bayesian Analysis of Two-Piece Distributions Based on the Scale Mixtures of Normal Family

The current paper seeks to present a Bayesian approach for the estimation of the parameters of the two-piece scale mixtures of normal distributions. This is a rich family of light/heavy-tailed symmetric/asymmetric distributions that includes, as a special case, the heavy-tailed scale mixtures of normal distributions, and is flexible in computations for modeling symmetric and asymmetric data. A Bayesian approach is possible from the specification of hierarchical representations of the proposed family. We illustrate the usefulness of our approach with both real and simulated data.