Power generalization of Chebyshev’s inequality – multivariate case

Katarzyna Budny

doi:10.21307/stattrans-2019-029

Power generalization of Chebyshev’s inequality – multivariate case

Katarzyna Budny Department of Mathematics, Cracow University of Economics, Poland ORCID:https://orcid.org/0000-0002-3683-0327 Statistics in Transition new series, vol. 20, 2019, 3, pages: 155-170 Published online: 30 August 2019 DOI 10.21307/stattrans-2019-029

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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.

KEYWORDS

multivariate Chebyshev’s inequality, Mahalanobis distance, multivariate normal distribution, multivariate t distribution

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