New results on perturbation-based copulas

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, Linz, Austria
Kolesárová Anna: Institute of Information Engineering, Automation and Mathematics, Faculty of Chemical and Food Technology, Slovak University of Technology, Bratislava, Slovakia
Šeliga Adam: Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovakia
Mesiar Radko: Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovakia, and Institute for Research and Applications of Fuzzy Modeling, NSC IT4Innovations, University of Ostrava, Czech Republic
Klement Erich Peter: Institute for Mathematical Methods in Medicine and Data Based Modeling, Johannes Kepler University, Linz, Austria

Dependence Modeling, 2021, vol. 9, issue 1, 347-373

Abstract: A prominent example of a perturbation of the bivariate product copula (which characterizes stochastic independence) is the parametric family of Eyraud-Farlie-Gumbel-Morgenstern copulas which allows small dependencies to be modeled. We introduce and discuss several perturbations, some of them perturbing the product copula, while others perturb general copulas. A particularly interesting case is the perturbation of the product based on two functions in one variable where we highlight several special phenomena, e.g., extremal perturbed copulas. The constructions of the perturbations in this paper include three different types of ordinal sums as well as flippings and the survival copula. Some particular relationships to the Markov product and several dependence parameters for the perturbed copulas considered here are also given.

Keywords: copula; dependence parameter; Eyraud-Farlie-Gumbel-Morgenstern copula; ordinal sum; perturbation (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:9:y:2021:i:1:p:347-373:n:12

DOI: 10.1515/demo-2021-0116

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