Stochastic orderings of multivariate elliptical distributions. (English) Zbl 1476.60043
Summary: For two \(n\)-dimensional elliptical random vectors X and Y, we establish an identity for \(\mathbb{E}[f(\mathbf{Y})]-\mathbb{E}[f(\mathbf{X})]\), 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.
MSC:
| 60E15 | Inequalities; stochastic orderings |
Keywords:
increasing convex order; multivariate elliptical distribution; multivariate normal distribution; supermodular order; usual stochastic orderSoftware:
QRMReferences:
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