Geodesic
On multivariate skewness and kurtosis
Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 3, pp. 675-679

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Let $X$ be a $d$-dimensional standardized random variable $(\mathbf{E}(X)=0,\operatorname{cov}(X)=1)$. Then for a multivariate analogue of skewness $s=\mathbf{E}(\|X\|^2X)$ and kurtosis $k=\mathbf{E}XX^TXX^T-(d+2)I$ we show that $\|s\|^2\le\operatorname{tr}k+2d$. For infinitly divisible distributions $\|s\|^2\le\operatorname{tr}k$.
Keywords: multivariate skewness, infinitely divisible distributions.
Mots-clés : kurtosis 
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     title = {On multivariate skewness and kurtosis},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     year = {1993},
     language = {en},
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T. F. Móri; V. K. Rohatgi; G. J. Szekely. On multivariate skewness and kurtosis. Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 3, pp. 675-679. http://geodesic.mathdoc.fr/item/TVP_1993_38_3_a20/