An Alternative Class of Multivariate Scale Mixtures of Skew-Normal Distributions

The normal distribution is a routine assumption for the analysis of real data, but it may be unrealistic specially when the data present strong skewness, as well as heavy tails. Following Branco & Dey (2001) and Arellano-Valle et al. (2007), this article develops a new class of multivariate scale mixtures of skew-normal distributions which includes the skew-normal (and the normal) distribution as a special case. The main advantage of these class of distributions is that they have a nice hierarchical representation that allows the implementation of Markov chain Monte Carlo (MCMC) methods to simulate samples from the joint posterior distribution. Analytical forms of the densities are obtained and distributional properties of the proposed class are also studied. In order to examine the robust aspects of this flexible class, against outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback-Leibler divergence. Results obtained from simulated and real data sets are reported illustrating the usefulness of the proposed methodology.