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.

中文翻译：

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多元椭圆分布的随机排序

两个n维椭圆随机向量X和是, 我们为$\mathbb{E}[f({\bf Y})]- \mathbb{E}[f({\bf X})]$， 在哪里$f\,{:}\, \mathbb{R}^n \rightarrow \mathbb{R}$满足一些规律性条件。使用这个恒等式，我们提供了一种统一的方法来推导根据几个主要的积分随机顺序对多元椭圆随机向量进行分类的充分和必要条件。因此，我们通过将该方法应用于多元椭圆分布来获得新的不等式。结果概括了文献中多元正态随机向量的相应结果。