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Extensions of Pearson’s inequality between skewness and kurtosis to multivariate cases

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  • Ogasawara, Haruhiko

Abstract

An extension of Pearson’s inequality between squared skewness and kurtosis to the case with three possibly distinct variables is obtained. A similar extension to the multivariate analogue of skewness defined by Mardia (1970) is also derived.

Suggested Citation

  • Ogasawara, Haruhiko, 2017. "Extensions of Pearson’s inequality between skewness and kurtosis to multivariate cases," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 12-16.
    • Handle: RePEc:eee:stapro:v:130:y:2017:i:c:p:12-16
    DOI: 10.1016/j.spl.2017.07.003
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    References listed on IDEAS

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    1. Klaassen, Chris A. J. & Mokveld, Philip J. & van Es, Bert, 2000. "Squared skewness minus kurtosis bounded by 186/125 for unimodal distributions," Statistics & Probability Letters, Elsevier, vol. 50(2), pages 131-135, November.
    2. Rohatgi, Vijay K. & Székely, Gábor J., 1989. "Sharp inequalities between skewness and kurtosis," Statistics & Probability Letters, Elsevier, vol. 8(4), pages 297-299, September.
    3. Ananda Sen, 2012. "On the Interrelation Between the Sample Mean and the Sample Variance," The American Statistician, Taylor & Francis Journals, vol. 66(2), pages 112-117, May.
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    Cited by:

    1. Loperfido, Nicola, 2021. "Some theoretical properties of two kurtosis matrices, with application to invariant coordinate selection," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    2. Loperfido, Nicola, 2020. "Some remarks on Koziol’s kurtosis," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    3. Baishuai Zuo & Narayanaswamy Balakrishnan & Chuancun Yin, 2023. "An analysis of multivariate measures of skewness and kurtosis of skew-elliptical distributions," Papers 2311.18176, arXiv.org.
    4. Masayuki Ando & Masaaki Fukasawa, 2023. "When to efficiently rebalance a portfolio," Papers 2308.08745, arXiv.org.

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