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Teoriya Veroyatnostei i ee Primeneniya, 1993, Volume 38, Issue 3, Pages 675–679 (Mi tvp4007)  
This article is cited in 69 scientific papers (total in 69 papers)

Short Communications

On multivariate skewness and kurtosis

T. F. Mória, V. K. Rohatgib, G. J. Szekelyb

a Eötvös University, Budapest, Hungary
b Bowling Green State University, Bowling Green, USA
Full-text PDF (1087 kB) Citations (69)
Abstract: 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, kurtosis, infinitely divisible distributions.
Received: 14.03.1991
English version:
Theory of Probability and its Applications, 1993, Volume 38, Issue 3, Pages 547–551
DOI: https://doi.org/10.1137/1138055
Bibliographic databases:
Document Type: Article
Language: English
Citation: T. F. Móri, V. K. Rohatgi, G. J. Szekely, “On multivariate skewness and kurtosis”, Teor. Veroyatnost. i Primenen., 38:3 (1993), 675–679; Theory Probab. Appl., 38:3 (1993), 547–551
Citation in format AMSBIB
\Bibitem{MorRohSze93}
\by T.~F.~M\'ori, V.~K.~Rohatgi, G.~J.~Szekely
\paper On multivariate skewness and kurtosis
\jour Teor. Veroyatnost. i Primenen.
\yr 1993
\vol 38
\issue 3
\pages 675--679
\mathnet{http://mi.mathnet.ru/tvp4007}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1404679}
\zmath{https://zbmath.org/?q=an:0807.60020}
\transl
\jour Theory Probab. Appl.
\yr 1993
\vol 38
\issue 3
\pages 547--551
\crossref{https://doi.org/10.1137/1138055}
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    • This publication is cited in the following 69 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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