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Power Generalization Of Chebyshev’S Inequality – Multivariate Case

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  • Budny Katarzyna

    (Department of Mathematics, Cracow University of Economics, Cracow, Poland .)

Abstract

In the paper some multivariate power generalizations of Chebyshev’s inequality and their improvements will be presented with extension to a random vector with singular covariance matrix. Moreover, for these generalizations, the cases of the multivariate normal and the multivariate t distributions will be considered. Additionally, some financial application will be presented.

Suggested Citation

  • Budny Katarzyna, 2019. "Power Generalization Of Chebyshev’S Inequality – Multivariate Case," Statistics in Transition New Series, Statistics Poland, vol. 20(3), pages 155-170, September.
    • Handle: RePEc:vrs:stintr:v:20:y:2019:i:3:p:155-170:n:1
    DOI: 10.21307/stattrans-2019-029
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    References listed on IDEAS

    as
    1. Navarro, Jorge, 2014. "Can the bounds in the multivariate Chebyshev inequality be attained?," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 1-5.
    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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