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.
↧
