On Multivariate Skewness and Kurtosis

Sreenivasa Rao Jammalamadaka (), Emanuele Taufer () and Gyorgy H. Terdik ()
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Sreenivasa Rao Jammalamadaka: University of California
Emanuele Taufer: University of Trento
Gyorgy H. Terdik: University of Debrecen

Sankhya A: The Indian Journal of Statistics, 2021, vol. 83, issue 2, No 6, 607-644

Abstract: Abstract 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.

Keywords: Multivariate skewness; Multivariate kurtosis; Cumulant vectors; Interconnections between different measures; Symmetric and skew multivariate distributions; 62H05; 60E05; 60E10 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s13171-020-00211-6

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