Article ID Journal Published Year Pages File Type
1146502 Journal of Multivariate Analysis 2012 15 Pages PDF
Abstract

The main objective of this work is to calculate and compare different measures of multivariate skewness for the skew-normal family of distributions. For this purpose, we consider the Mardia (1970) [10], Malkovich and Afifi (1973) [9], Isogai (1982) [17], Srivastava (1984) [15], Song (2001) [14], Móri et al. (1993) [11], Balakrishnan et al. (2007) [3] and Kollo (2008) [7] measures of skewness. The exact expressions of all measures of skewness, except for Song’s, are derived for the family of skew-normal distributions, while Song’s measure of shape is approximated by the use of delta method. The behavior of these measures, their similarities and differences, possible interpretations, and their practical use in testing for multivariate normal are studied by evaluating their power in the case of some specific members of the multivariate skew-normal family of distributions.

► We calculate different measures of multivariate skewness for skew-normal distributions. ► Exact expressions of 7 measures of skewness are derived for multivariate skew-normal distributions. ► Behavior, differences, interpretations and tests for normality against skew-normal on all these measures are studied and their power properties are assessed.

Related Topics
Physical Sciences and Engineering Mathematics Numerical Analysis
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