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

Author

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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)

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.

Suggested Citation

  • Saminger-Platz Susanne & Kolesárová Anna & Šeliga Adam & Mesiar Radko & Klement Erich Peter, 2024. "On comprehensive families of copulas involving the three basic copulas and transformations thereof," Dependence Modeling, De Gruyter, vol. 12(1), pages 1-36.
    • Handle: RePEc:vrs:demode:v:12:y:2024:i:1:p:36:n:1001
    DOI: 10.1515/demo-2024-0007
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    References listed on IDEAS

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