Abstract In this paper, (positive) linear stochastic orderings of random vectors X and Y having scale mixtures of the multivariate skew-normal distribution are studied. Necessary and sufficient convenient conditions for a ⊤ X to be less than a ⊤ Y , when a is a vector of positive values, in the sense of usual, convex and increasing convex stochastic orders are grasped. The results are potentially applied to conduct some stochastic comparisons of weekly returns of developed markets and emerging markets. We demonstrate that the family of distributions is ordered in the stop-loss and the second degree stochastic dominance orders in terms of the correlation coefficients of the underlying random vectors. A possible application of one of the results in the reliability analysis of series and parallel systems is supplied.

中文翻译：

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多元偏态正态分布的尺度混合的线性排序

摘要 在本文中，研究了具有多元偏态正态分布的尺度混合的随机向量 X 和 Y 的（正）线性随机排序。a ⊤ X 小于a ⊤ Y 的充要充分便利条件，当a 为正值向量时，掌握了通常意义上的凸随机阶和递增凸随机阶。结果可能用于对发达市场和新兴市场的每周回报进行一些随机比较。我们证明了分布族在止损和二级随机优势顺序中根据基础随机向量的相关系数进行排序。提供了其中一个结果在串联和并联系统可靠性分析中的可能应用。