Statistical applications of the multivariate skew-normal distribution

Azzalini & Dalla Valle (1996) have recently discussed the multivariate skew-normal distribution which extends the class of normal distributions by the addition of a shape parameter. The first part of the present paper examines further probabilistic properties of the distribution, with special emphasis on aspects of statistical relevance. Inferential and other statistical issues are discussed in the following part, with applications to some multivariate statistics problems, illustrated by numerical examples. Finally, a further extension is described which introduces a skewing factor of an elliptical density.

💡 Research Summary

The paper provides a comprehensive treatment of the multivariate skew‑normal (MSN) distribution, a flexible extension of the multivariate normal that incorporates a shape (or skewness) vector α. Beginning with a precise definition, the authors write the density as
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