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Mathematics > Probability

arXiv:1812.07850 (math)
[Submitted on 19 Dec 2018 (v1), last revised 18 Nov 2019 (this version, v5)]

Title:Constructing copulas from shock models with imprecise distributions

Authors:Matjaž Omladič, Damjan Škulj
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Abstract: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 Omladič 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.
Subjects: Probability (math.PR)
ACM classes: G.3
Cite as: arXiv:1812.07850 [math.PR]
  (or arXiv:1812.07850v5 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1812.07850
Related DOI: https://doi.org/10.1016/j.ijar.2019.11.009

Submission history

From: Damjan Škulj [view email]
[v1] Wed, 19 Dec 2018 10:01:09 UTC (19 KB)
[v2] Mon, 3 Jun 2019 08:23:00 UTC (51 KB)
[v3] Wed, 12 Jun 2019 14:51:12 UTC (51 KB)
[v4] Mon, 19 Aug 2019 06:53:17 UTC (50 KB)
[v5] Mon, 18 Nov 2019 08:42:27 UTC (51 KB)
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