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Statistical applications of the multivariate skew normal distribution. (English) Zbl 0924.62050
Summary: A. Azzalini and A. Dalla Valle [Biometrika 83, No. 4, 715-726 (1996; Zbl 0885.62062)] 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.

MSC:
62H10 Multivariate distribution of statistics
62H05 Characterization and structure theory for multivariate probability distributions; copulas
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