Stochastic Orderings of Multivariate Elliptical Distributions

10/16/2019

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by   Chuancun Yin, et al.

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Let X and X be two n-dimensional elliptical random vectors, we establish an identity for E[f( Y)]-E[f( X)], where f: R^n →R fulfilling some regularity conditions. Using this identity we provide a unified derivation of 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 it to multivariate elliptical distributions. The results generalize the corresponding ones for multivariate normal random vectors in the literature.