Document Type

Article

Source of Publication

Mathematics

Publication Date

6-1-2024

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 (Formula presented.). It includes numerous examples and discusses the admissible range of parameter (Formula presented.), 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, (Formula presented.), 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, (Formula presented.) -inversion, and the moment copula method.

ISSN

2227-7390

Publisher

MDPI AG

Volume

12

Issue

11

Disciplines

Mathematics

Keywords

bivariate copula, copula moments, Fréchet–Hoeffding limit, maximum likelihood, ratio copula, singularity, ρ-inversion

Scopus ID

85195905740

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Indexed in Scopus

yes

Open Access

yes

Open Access Type

Gold: This publication is openly available in an open access journal/series

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Included in

Mathematics Commons

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