Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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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)
  • Received : 2017.10.24
  • Accepted : 2018.01.19
  • Published : 2018.03.31
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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.

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Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

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