Abstract
We use the measure of multivariate kurtosis introduced by Mardia to define an upper bound for the probability that the Mahalanobis distance of a random vector from its mean is greater or equal than a given value. The bound improves on a similar one, based on Markov’s theorem, and generalizes to the multivariate case an inequality which appears in several textbooks. It might be applied whenever the distribution of the Mahalanobis distance of a random vector from its mean is not easily computable, as it is often the case in finance and actuarial sciences.
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Acknowledgements
The Author wish to thank Prof. Domenico Piccolo for the encouragement.
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Loperfido, N. (2014). A Probability Inequality Related to Mardia’s Kurtosis. In: Perna, C., Sibillo, M. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-05014-0_30
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DOI: https://doi.org/10.1007/978-3-319-05014-0_30
Publisher Name: Springer, Cham
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