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.

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

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