Parameterized transformations and truncation: When is the result a copula?

Saminger‐Platz, Susanne; Kolesárová, Anna; Šeliga, Adam; Mesiar, Radko; Klement, Erich Peter

doi:10.1016/j.cam.2023.115340

Journal of Computational and Applied Mathematics

2024

DOI: 10.1016/j.cam.2023.115340

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Parameterized transformations and truncation: When is the result a copula?

Susanne Saminger‐Platz

Anna Kolesárová

Adam Šeliga

et al.

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

Saminger-Platz,

Kolesárová,

Šeliga

et al. 2024

Dependence Modeling

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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.

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

Saminger-Platz,

Kolesárová,

Šeliga

et al. 2024

Dependence Modeling

View full text Add to dashboard Cite

show abstract

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Parameterized transformations and truncation: When is the result a copula?

Cited by 1 publication

References 61 publications

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

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

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