A new scheme for simple asymmetric bivariate copulas and applications

Document Type

Article

Source of Publication

AIMS Mathematics

Publication Date

10-28-2025

Abstract

Bivariate copulas play a central role in modeling the dependence structure between two random variables and serve as a fundamental tool in various applied fields. In this article, we develop a new theoretical framework aimed at constructing simple asymmetric bivariate copulas of the form C(u, v) = uv [ϕ(v) + u(1 − ϕ(v))], (u, v) ∈ [0, 1]2. This framework relies on a tuning univariate function to achieve the desired asymmetry. We study this pioneering scheme, emphasizing its theoretical foundations, and illustrating it with several examples. More precisely, we establish important properties of the proposed copulas and derive analytical expressions for concordance measures such as Spearman’s rho, Kendall’s tau, Gini’s gamma, and Blomqvist’s beta. In addition, we investigate the estimation procedure for the dependence parameter using the maximum likelihood approach. Finally, we conduct a simulation study to evaluate the performance of the proposed estimator. A real climatological dataset from the city of Abu Dhabi is used to demonstrate the applicability of the proposed copulas, with very convincing results.

ISSN

2473-6988

Publisher

American Institute of Mathematical Sciences (AIMS)

Volume

10

Issue

10

First Page

24602

Last Page

24626

Disciplines

Mathematics

Keywords

asymmetric copulas, concordance measures, dependence models, maximum likelihood method

Scopus ID

105020767763

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

This document is currently not available here.

Share

COinS