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On Multivariate Skewness and Kurtosis

Author

Listed:
  • Sreenivasa Rao Jammalamadaka

    (University of California)

  • Emanuele Taufer

    (University of Trento)

  • Gyorgy H. Terdik

    (University of Debrecen)

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.

Suggested Citation

  • Sreenivasa Rao Jammalamadaka & Emanuele Taufer & Gyorgy H. Terdik, 2021. "On Multivariate Skewness and Kurtosis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 607-644, August.
    • Handle: RePEc:spr:sankha:v:83:y:2021:i:2:d:10.1007_s13171-020-00211-6
    DOI: 10.1007/s13171-020-00211-6
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