On comprehensive families of copulas involving the three basic copulas and transformations thereof

Saminger-Platz Susanne (), Kolesárová Anna (), Šeliga Adam (), Mesiar Radko () and Klement Erich Peter ()
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Saminger-Platz Susanne: Institute for Mathematical Methods in Medicine and Data Based Modeling, Johannes Kepler University, 4040 Linz, Austria
Kolesárová Anna: Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, 81107 Bratislava, Slovakia
Šeliga Adam: Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, 81107 Bratislava, Slovakia
Mesiar Radko: Institute for Research and Applications of Fuzzy Modeling, NSC IT4Innovations, University of Ostrava, 70103 Ostrava, Czech Republic
Klement Erich Peter: Institute for Mathematical Methods in Medicine and Data Based Modeling, Johannes Kepler University, 4040 Linz, Austria

Dependence Modeling, 2024, vol. 12, issue 1, 36

Abstract: Comprehensive families of copulas including the three basic copulas (at least as limit cases) are useful tools to model countermonotonicity, independence, and comonotonicity of pairs of random variables on the same probability space. In this contribution, we study how the transition from a (basic) copula to a copula modeling a different dependence behavior can be realized by means of ordinal sums based on one of the three basic copulas, perturbing one of the three basic copulas (considering some appropriate parameterized transformations) and truncating the results using the Fréchet-Hoeffding bounds. We provide results and examples showing the flexibility and the restrictions for obtaining new copulas or comprehensive families and illustrate the development of their dependence parameters.

Keywords: bivariate copula; ordinal sum of copulas; transformation of copula; comprehensive family of copulas; dependence measure (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:12:y:2024:i:1:p:36:n:1001

DOI: 10.1515/demo-2024-0007

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