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Research Article | Open Access

A compendium of expressions for dependence measures of bivariate copulas

Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
Department of Mathematics and Statistics, University of Zambia, Lusaka, Zambia; vnawa@yahoo.com
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Abstract

Copulas are important because they allow for modeling and analyzing the dependence structure between random variables, providing insights into complex relationships beyond linear correlations. In this paper, we produced a compendium of expressions for four of the most popular dependence measures of bivariate copulas. Over twenty-five families of bivariate copulas were considered.

Keywords

Blomqvist's β∗Hoeffding's Φ2Kendall's τSpearman's ρ
CLC number: 62E99

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AIMS Mathematics
Volume 10 Issue 9,
September 2025
Pages 22336-22381
DOI: 10.3934/math.2025995

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Cite this article:
Nadarajah S, Nawa V. A compendium of expressions for dependence measures of bivariate copulas. AIMS Mathematics, 2025, 10(9): 22336-22381. https://doi.org/10.3934/math.2025995

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Received: 08 August 2025
Revised: 09 September 2025
Accepted: 15 September 2025
Published: 26 September 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)