Abstract

Andrews and Mallows (J R Stat Soc 36:99–102, 1974) discussed a class of robust distributions as scale mixtures of normal (SMN) distributions, which contains a group of thick-tailed distributions. Their work was extended by Branco and Dey (J Multivariate Anal 79:99–113, 2001), introducing the class of scale mixtures of skew-normal (SMSN) distributions, which includes the former class by the introduction of a parameter regulating skewness. In this chapter, we discuss some properties of the SMSN distributions in the multivariate setting. The main virtue of the members of this family is that they are easy to simulate from and they also lend themselves to an EM-type algorithm for maximum likelihood estimation. Results obtained from simulated and a real data set are reported illustrating the usefulness of the proposed distributions.

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