Skew-Normal/Independent Distributions, with Applications

Normal/independent distributions are often used as a challenging family for statistical procedures of symmetrical data. In this article, we have defined a skewed version of these distributions in the multivariate setting and we have derived several of its properties. The main virtue of the members of this family of distributions is that they are easy to simulate from and they also lend themselves to the Monte Carlo EM algorithm for maximum likelihood estimation. For multivariate skewed responses, the EM-type algorithm has been discussed with emphasis on the skew-t, on the skew-slash, and on the skew-contaminated normal distributions. Results obtained from simulated and real data sets are reported illustrating the usefulness of the proposed methodology.