On Multivariate Skewness and Kurtosis
Copyright policy )On Multivariate Skewness and Kurtosis
Summary: Let \(X\) be a \(d\)-dimensional standardized random variable \(({\mathbf E}(X) = 0\), \(\text{cov}(X) = 1)\). Then for a multivariate analogue of skewness \(s = {\mathbf E}(\| X \|^ 2 X)\) and kurtosis \(k = {\mathbf E} XX^ T XX^ T - (d + 2)I\) we show that \(\| s\|^ 2 \leq \text{tr }k + 2d\). For infinitely divisible distributions, \(\| s\|^ 2 \leq \text{tr }k\).
kurtosis, Infinitely divisible distributions; stable distributions, multivariate skewness, Characterization and structure theory for multivariate probability distributions; copulas, infinitely divisible distributions
kurtosis, Infinitely divisible distributions; stable distributions, multivariate skewness, Characterization and structure theory for multivariate probability distributions; copulas, infinitely divisible distributions
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