On multivariate skewness and kurtosis. (English) Zbl 1512.62054
Summary: A unified treatment of all currently available cumulant-based indexes of multivariate skewness and kurtosis is provided here, expressing them in terms of the third and fourth-order cumulant vectors respectively. Such a treatment helps reveal many subtle features and inter-connections among the existing indexes as well as some deficiencies, which are hitherto unknown. Computational formulae for obtaining these measures are provided for spherical and elliptically-symmetric, as well as skew-symmetric families of multivariate distributions, yielding several new results and a systematic exposition of many known results.
MSC:
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
| 60E05 | Probability distributions: general theory |
| 62H10 | Multivariate distribution of statistics |
Keywords:
multivariate skewness; multivariate kurtosis; cumulant vectors; interconnections between different measures; symmetric and skew multivariate distributionsReferences:
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