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Improved probability inequalities for Mardia’s coefficient of kurtosis

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  • Budny, Katarzyna

Abstract

We provide a probability inequality which, for some classes of multivariate distributions, improves on probability inequalities related to Mardia’s coefficient of kurtosis. Furthermore, we extend our result to the case of a random vector with singular covariance matrix.

Suggested Citation

  • Budny, Katarzyna, 2022. "Improved probability inequalities for Mardia’s coefficient of kurtosis," Statistics & Probability Letters, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:stapro:v:191:y:2022:i:c:s0167715222001808
    DOI: 10.1016/j.spl.2022.109664
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    References listed on IDEAS

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    1. Haruhiko Ogasawara, 2020. "Some Improvements on Markov's Theorem with Extensions," The American Statistician, Taylor & Francis Journals, vol. 74(3), pages 218-225, July.
    2. Katarzyna Budny, 2016. "An extension of the multivariate Chebyshev's inequality to a random vector with a singular covariance matrix," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(17), pages 5220-5223, September.
    3. Lin, Pi-Erh, 1972. "Some characterizations of the multivariate t distribution," Journal of Multivariate Analysis, Elsevier, vol. 2(3), pages 339-344, September.
    4. Budny, Katarzyna, 2014. "A generalization of Chebyshev’s inequality for Hilbert-space-valued random elements," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 62-65.
    5. Jorge Navarro, 2016. "A very simple proof of the multivariate Chebyshev's inequality," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(12), pages 3458-3463, June.
    Full references (including those not matched with items on IDEAS)

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