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Final solution to the problem of relating a true copula to an imprecise copula

机译：最终解决一个真正的copula与不精确的copula的问题

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In this paper we solve in the negative the problem proposed in this journal (Montes et al. (2015) [13]) whether an order interval defined by an imprecise copula contains a copula. Namely, if C is a nonempty set of copulas, then (C) under bar = inf{C}(C is an element of C) and (C) over bar = sup{C}(C is an element of C) are quasi-copulas and the pair ((C) under bar, (C) over bar) is an imprecise copula according to the definition introduced in the cited paper, following the ideas of p-boxes. We show that there is an imprecise copula (A, B) in this sense such that there is no copula Cwhatsoever satisfying A = C = B. So, it is questionable whether the proposed definition of the imprecise copula is in accordance with the intentions of the initiators. Our methods may be of independent interest: We upgrade the ideas of Dibala et al. (2016) [7] where possibly negative volumes of quasi-copulas as defects from being copulas were studied. (C) 2019 Elsevier B.V. All rights reserved.
机译：在本文中，我们解决了在本期刊（Montes等）所提出的问题中的负面（2015）[13]）是否由不精确的copula定义的订单间隔包含一个副本。即，如果c是一个非空的copulas集，那么（c）在bar = inf {c}（c是c）和（c）over bar = sup {c}（c是c的元素）是根据P-Box的思想，拟链式和杆下方的杆（c）（c）＆byb）是根据引文中引入的定义的不精确谱系。我们表明，在这种意义上存在不精确的copula（a，b），使得不满足<= c <= b的Copula Cwhatever。所以，拟议的opula的定义是符合的发起人的意图。我们的方法可能是独立的兴趣：我们升级了Dibala等人的想法。 （2016）[7]在其中研究了作为缺陷的拟额外量的额外量的含量。 （c）2019 Elsevier B.v.保留所有权利。

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