The omnipotence of copulas when modeling dependence given marg\-inal distributions in a multivariate stochastic situation is assured by the Sklar's theorem. Montes et al.\ (2015) suggest the notion of what they call an \emph{imprecise copula} that brings some of its power in bivariate case to the imprecise setting. When there is imprecision about the marginals, one can model the available information by means of $p$-boxes, that are pairs of ordered distribution functions. By analogy they introduce pairs of bivariate functions satisfying certain conditions. In this paper we introduce the imprecise versions of some classes of copulas emerging from shock models that are important in applications. The so obtained pairs of functions are not only imprecise copulas but satisfy an even stronger condition. The fact that this condition really is stronger is shown in Omladi\v{c} and Stopar (2019) thus raising the importance of our results. The main technical difficulty in developing our imprecise copulas lies in introducing an appropriate stochastic order on these bivariate objects.

中文翻译：

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从分布不精确的冲击模型构建 copula

Sklar 定理保证了在对多元随机情况下给定边际分布的依赖性建模时，copula 的全能性。Montes et al.\ (2015) 提出了他们所谓的 \emph {imprecise copula} 的概念，它将双变量情况下的一些力量带到了不精确的环境中。当边缘不精确时，可以通过 $p$-boxes 对可用信息进行建模，即一对有序分布函数。通过类比，它们引入了满足特定条件的双变量函数对。在本文中，我们介绍了从冲击模型中出现的某些类型的 copula 的不精确版本，它们在应用中很重要。如此获得的函数对不仅是不精确的联结，而且满足更强的条件。Omladi\v{c} 和 Stopar (2019) 显示了这种条件确实更强的事实，从而提高了我们结果的重要性。开发我们不精确的 copula 的主要技术困难在于在这些双变量对象上引入适当的随机顺序。