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http://dx.doi.org/10.29220/CSAM.2018.25.2.109

Multivariate measures of skewness for the scale mixtures of skew-normal distributions  

Kim, Hyoung-Moon (Department of Applied Statistics, Konkuk University)
Zhao, Jun (Department of Applied Statistics, Konkuk University)
Publication Information
Communications for Statistical Applications and Methods / v.25, no.2, 2018 , pp. 109-130 More about this Journal
Abstract
Several measures of multivariate skewness for scale mixtures of skew-normal distributions are derived. As a special case, those of multivariate skew-t distribution are considered in detail. Furthermore, the similarities, differences, and behavior of these measures are explored for cases of some specific members of the multivariate skew-normal and skew-t distributions using a simulation study. Since some measures are vectors, it is better to take all measures in the same scale when comparing them. In order to attain such a set of comparable indices, the sample version is considered for each of the skewness measures that are taken as test statistics for the hypothesis of t distribution against skew-t distribution. An application is reported for the data set consisting of 71 total glycerol and magnesium contents in Grignolino wine.
Keywords
scale mixtures; skew-normal; skew-t; multivariate skewness;
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