Abstract A classical result of Slepian (1962) for the normal distribution and extended by Das Guptas et al. (1972) for elliptical distributions gives one-sided (lower orthant) comparison criteria for the distributions with respect to the (generalized) correlations. Muller and Scarsini (2000) established that the ordering conditions even characterize the stronger supermodular ordering in the normal case. In the present paper, we extend this result to elliptical distributions. We also derive a similar comparison result for the directionally convex ordering of elliptical distributions. As application, we obtain several results on risk bounds in elliptical classes of risk models under restrictions on the correlations or on the partial correlations. Furthermore, we obtain extensions and strengthenings of recent results on risk bounds for various classes of partially specified risk factor models with elliptical dependence structure of the individual risks and the common risk factor. The moderate dependence assumptions on this type of models allow flexible applications and, in consequence, are relevant for improved risk bounds in comparison to the marginal based standard bounds.

中文翻译：

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应用到风险界限的椭圆分布的排序结果

摘要 Slepian (1962) 对正态分布的经典结果并由 Das Guptas 等人扩展。(1972) 为椭圆分布给出了关于（广义）相关性的分布的单边（下orthant）比较标准。Muller 和 Scarsini (2000) 确定排序条件甚至表征了正常情况下更强的超模排序。在本文中，我们将此结果扩展到椭圆分布。我们还为椭圆分布的方向凸排序得出了类似的比较结果。作为应用，我们在相关性或偏相关性的限制下，在风险模型的椭圆类中获得了风险界限的几个结果。此外，我们获得了对各种类别的部分指定风险因素模型的风险界限的最新结果的扩展和加强，这些模型具有个人风险和共同风险因素的椭圆依赖结构。对此类模型的适度依赖假设允许灵活应用，因此与基于边际的标准界限相比，与改进的风险界限相关。