This paper proposes a unified class of generalized location-scale mixture of multivariate elliptical distributions and studies integral stochastic orderings of random vectors following such distributions. Given a random vector $\boldsymbol{Z}$, independent of $\boldsymbol{X}$ and $\boldsymbol{Y}$, the scale parameter of this class of distributions is mixed with a function $\alpha(\boldsymbol{Z})$ and its skew parameter is mixed with another function $\beta(\boldsymbol{Z})$. Sufficient (and necessary) conditions are established for stochastically comparing different random vectors stemming from this class of distributions by means of several stochastic orders including the usual stochastic order, convex order, increasing convex order, supermodular order, and some related linear orders. Two insightful assumptions for the density generators of elliptical distributions, aiming to control the generators' tail, are provided to make stochastic comparisons among mixed-elliptical vectors. Some applications in applied probability and actuarial science are also provided as illustrations on the main findings.
翻译:本文提出一个统一的多变椭圆分布和研究随机矢量在这种分布之后的随机矢量整体随机排序的通用位置比例混合物类别。如果使用一个不受$\boldsymbol{X}$和$\boldsymbol{Y}$独立的随机矢量 $\ boldsymbol{Y} 美元,则该类分布的比重参数与一个函数$alpha(\boldsymbol}$)和它的斜度参数混在一起,与另一个函数$\beta(\boldsymbol}$)混在一起。为通过若干随机排序的随机矢量(和美元)建立足够的(和必要的)条件,以便通过包括通常的随机顺序、convex顺序、增加的convex顺序、超模调和一些相关的线性顺序等方法对来自该类分布的不同随机矢量矢量进行分辨比较。为控制发电机尾部提供了两种有洞察力的假设,目的是对来自该类矢量矢量的矢量矢量进行比较。还提供了一些主要的实验性应用。</s>