Abstract Stochastic orders are mathematical methods allowing the comparison of random quantities. Probably the most usual one is stochastic dominance, which is based on the comparison of univariate cumulative distribution functions. Although it has been commonly applied, it does not consider the dependence between the random variables. This paper introduces a new stochastic order that slightly modifies stochastic dominance preserving its philosophy but taking into account the dependence between the random variables. This new stochastic order is based on the comparison of the cumulative distribution functions of the differences of the random variables, and it is closely related to regret theory. Since it uses the joint distribution, the copula gathering the dependence plays a crucial role. We present a theoretical study of this new stochastic order, delving into its connection with regret theory, investigating the role of the copula that links the random variables and establishing some connections with stochastic dominance.

中文翻译：

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涉及依赖的随机支配的修改版本

摘要 随机阶数是允许比较随机量的数学方法。可能最常见的是随机优势，它基于单变量累积分布函数的比较。虽然它已经被普遍应用，但它没有考虑随机变量之间的依赖关系。本文介绍了一种新的随机顺序，该顺序略微修改了随机优势，保留了其哲学，但同时考虑了随机变量之间的相关性。这种新的随机顺序是基于随机变量差异的累积分布函数的比较，与后悔理论密切相关。由于它使用联合分布，因此收集依赖的 copula 起着至关重要的作用。我们对这种新的随机顺序进行了理论研究，