Skew Scale Mixture of Normal Distributions: Properties and Estimation

Scale mixture of normal 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 and we have derived several of its probabilistic and inferential properties. The main virtue of the members of this family of distributions is that they are easy to simulate from and they also supply genuine EM algorithms for maximum likelihood estimation. For univariate skewed responses, the EM-type algorithm has been discussed with emphasis on the skew-t, skew-slash, skew-contaminated normal and skew-exponential power distributions. Some simplifying and unifying results are also noted with the Fisher informating matrix, which is derived in closed form for some distributions in the family. Results obtained from simulated and real data sets are reported illustrating the usefulness of the proposed methodology. The main conclusion in reanalyzing a data set previously studied is that the models so far entertained are clearly not the most adequate ones.