On the Ratio-Type Family of Copulas

Farid El Ktaibi (), Rachid Bentoumi and Mhamed Mesfioui ()
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Farid El Ktaibi: Department of Mathematics and Statistics, Zayed University, Abu Dhabi 144534, United Arab Emirates
Rachid Bentoumi: Department of Mathematics and Statistics, Zayed University, Abu Dhabi 144534, United Arab Emirates
Mhamed Mesfioui: Département de Mathématiques et d’Informatique, Université du Québec à Trois-Rivières, Trois-Rivières, QC G9A 5H7, Canada

Mathematics, 2024, vol. 12, issue 11, 1-17

Abstract: Investigating dependence structures across various fields holds paramount importance. Consequently, the creation of new copula families plays a crucial role in developing more flexible stochastic models that address the limitations of traditional and sometimes impractical assumptions. The present article derives some reasonable conditions for validating a copula of the ratio-type form u v / ( 1 − θ f ( u ) g ( v ) ) . It includes numerous examples and discusses the admissible range of parameter θ , showcasing the diversity of copulas generated through this framework, such as Archimedean, non-Archimedean, positive dependent, and negative dependent copulas. The exploration extends to the upper bound of a general family of copulas, u v / ( 1 − θ ϕ ( u , v ) ) , and important properties of the copula are discussed, including singularity, measures of association, tail dependence, and monotonicity. Furthermore, an extensive simulation study is presented, comparing the performance of three different estimators based on maximum likelihood, ρ -inversion, and the moment copula method.

Keywords: bivariate copula; ratio copula; Fréchet–Hoeffding limit; singularity; maximum likelihood; ? -inversion; copula moments (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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