On Multivariate Skewness and Kurtosis

Sankhya A - 2021
S. Rao Jammalamadaka1, Emanuele Taufer2, György Terdik3
1University of California, Santa Barbara, CA USA
2University of Trento, Trento, Italy
3University of Debrecen, Debrecen, Hungary

Tóm tắt

AbstractA 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.

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