A generalized multivariate kurtosis ordering and its applications

Jin Wang, Weihua Zhou

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


It has been commonly admitted that the meaning of a descriptive feature of distributions is given by an ordering and that the measures for this feature are meaningful only if they preserve the ordering. However, while many multivariate kurtosis measures have been introduced, multivariate kurtosis orderings have received relatively little investigation. In this paper, we propose and study a generalized multivariate kurtosis ordering. Under some conditions, this ordering is affine invariant and determines elliptically symmetric distributions within affine equivalence. Some special cases of the generalized ordering provide the kurtosis orderings for various existing multivariate kurtosis measures. Those kurtosis orderings are applied to explore the relationships of the multivariate kurtosis measures. Some other applications of the generalized multivariate kurtosis ordering are also given.

Original languageEnglish (US)
Pages (from-to)169-180
Number of pages12
JournalJournal of Multivariate Analysis
StatePublished - May 2012


  • Depth function
  • Kurtosis
  • Multivariate quantile function
  • Ordering
  • Spread functional

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


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