%0 Generic %1 yin2019stochastic %A Yin, Chuancun %D 2019 %K elliptical multivariate normal statistics %T Stochastic Orderings of Multivariate Elliptical Distributions %U http://arxiv.org/abs/1910.07158 %X Let $X$ and $X$ be two $n$-dimensional elliptical random vectors, we establish an identity for $Ef(Y)-Ef(X)$, where $f: \BbbR^n \BbbR$ 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.

@misc{yin2019stochastic, abstract = {Let ${\bf X}$ and ${\bf X}$ be two $n$-dimensional elliptical random vectors, we establish an identity for $E[f({\bf Y})]-E[f({\bf X})]$, where $f: \Bbb{R}^n \rightarrow \Bbb{R}$ 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.}, added-at = {2019-10-18T07:15:54.000+0200}, author = {Yin, Chuancun}, biburl = {https://www.bibsonomy.org/bibtex/2e5929505be2b830bb2e0a90fd3bf4f68/shabbychef}, description = {Stochastic Orderings of Multivariate Elliptical Distributions}, interhash = {a218b24ebff9ccf5b836f05473e79fd5}, intrahash = {e5929505be2b830bb2e0a90fd3bf4f68}, keywords = {elliptical multivariate normal statistics}, note = {cite arxiv:1910.07158Comment: 18 pages}, timestamp = {2019-10-18T07:15:54.000+0200}, title = {Stochastic Orderings of Multivariate Elliptical Distributions}, url = {http://arxiv.org/abs/1910.07158}, year = 2019 }