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, Sreenivasa Rao; Taufer, Emanuele; Terdik, Gyorgy H.. - In: SANKHYA. SERIES A. - ISSN 0976-836X. - 2021, 83:2(2021), pp. 607-644. [10.1007/s13171-020-00211-6]
On Multivariate Skewness and Kurtosis
Taufer, EmanueleSecondo
;
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 | |
|---|---|---|---|
|
2021 - Sankhya A - On multivariate skewness and kurtosis.pdf
accesso aperto
Tipologia:
Versione editoriale (Publisher’s layout)
Licenza:
Creative commons
Dimensione
3.84 MB
Formato
Adobe PDF
|
3.84 MB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
