On Multivariate Skewness and Kurtosis
S. Rao Jammalamadaka, Emanuele Taufer, György Terdik
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.
Topics & Concepts
KurtosisMultivariate statisticsSkewnessSkewCumulantMultivariate analysisExposition (narrative)MathematicsMultivariate normal distributionEconometricsStatisticsApplied mathematicsComputer scienceLiteratureTelecommunicationsArtStatistical Distribution Estimation and ApplicationsAdvanced Statistical Methods and ModelsFinancial Risk and Volatility Modeling