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.
On Multivariate Skewness and Kurtosis / Jammalamadaka, S. R.; Taufer, E.; Terdik, G. H.. - In: SANKHYA. SERIES A. - ISSN 0976-836X. - 2021:83(2021), pp. 607-644. [10.1007/s13171-020-00211-6]
On Multivariate Skewness and Kurtosis
Taufer E.;
2021-01-01
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.| File | Dimensione | Formato | |
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2021 - Sankhya A - On multivariate skewness and kurtosis.pdf
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