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Stochastic orderings of multivariate elliptical distributions

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  23 June 2021

Chuancun Yin
Chuancun Yin*
Affiliation:
Qufu Normal University
*
*Postal address: School of Statistics, Qufu Normal University, Qufu 273165, Shandong, China. Email address: ccyin@qfnu.edu.cn
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Abstract

For two n-dimensional elliptical random vectors X and Y, we establish an identity for $\mathbb{E}[f({\bf Y})]- \mathbb{E}[f({\bf X})]$, where $f\,{:}\, \mathbb{R}^n \rightarrow \mathbb{R}$ satisfies some regularity conditions. Using this identity we provide a unified method to derive sufficient and necessary conditions for classifying multivariate elliptical random vectors according to several main integral stochastic orders. As a consequence we obtain new inequalities by applying the method to multivariate elliptical distributions. The results generalize the corresponding ones for multivariate normal random vectors in the literature.

Keywords

Increasing convex ordermultivariate elliptical distributionmultivariate normal distributionsupermodular orderusual stochastic order

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Type
Original Article
Information
Journal of Applied Probability , Volume 58 , Issue 2 , June 2021 , pp. 551 - 568
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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