A compendium of expressions for dependence measures of bivariate copulas

Saralees Nadarajah; Victor Nawa; Saralees Nadarajah; Victor Nawa

doi:10.3934/math.2025995

AIMS Mathematics

2025, Volume 10, Issue 9: 22336-22381. doi: 10.3934/math.2025995

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A compendium of expressions for dependence measures of bivariate copulas

Saralees Nadarajah ^{1
,
,},
Victor Nawa ^{2
,}

1.
Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
2.
Department of Mathematics and Statistics, University of Zambia, Lusaka, Zambia; vnawa@yahoo.com

Received: 08 August 2025 Revised: 09 September 2025 Accepted: 15 September 2025 Published: 26 September 2025
MSC : 62E99

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.
- Blomqvist's $ \beta^{*} $,
- Hoeffding's $ \Phi^2 $,
- Kendall's $ \tau $,
- Spearman's $ \rho $
Citation: Saralees Nadarajah, Victor Nawa. A compendium of expressions for dependence measures of bivariate copulas[J]. AIMS Mathematics, 2025, 10(9): 22336-22381. doi: 10.3934/math.2025995

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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.

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