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Statistical Applications of the Multivariate Skew Normal Distribution

Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1999 · Vol. 61(3) · pp. 579–602

Adelchi Azzalini✉(University of Padua)Antonella Capitanio(University of Bologna)

Abstract

Summary Azzalini and Dalla Valle 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.

Statistical Distribution Estimation and Applications Advanced Statistical Methods and Models Optimal Experimental Design MethodsSkew normal distributionSkewMultivariate statisticsMultivariate normal distributionElliptical distributionNormal-Wishart distributionNormal distributionExtension (predicate logic)Statistical parameterMathematics