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New results on perturbation-based copulas

Author

Listed:
  • 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)

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.

Suggested Citation

  • Saminger-Platz Susanne & Kolesárová Anna & Šeliga Adam & Mesiar Radko & Klement Erich Peter, 2021. "New results on perturbation-based copulas," Dependence Modeling, De Gruyter, vol. 9(1), pages 347-373, January.
    • Handle: RePEc:vrs:demode:v:9:y:2021:i:1:p:347-373:n:12
    DOI: 10.1515/demo-2021-0116
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    References listed on IDEAS

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