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AppliedMath
Volume 4
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10.3390/appliedmath4010019
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Review

Four Measures of Association and Their Representations in Terms of Copulas

by
Michel Adès
1,
Serge B. Provost
2,* and
Yishan Zang
2
1
Département de Mathématiques, Université du Québec à Montréal, Montréal, QC H2X 3Y7, Canada
2
Department of Statistical and Actuarial Sciences, The University of Western Ontario, London, ON N6A 5B7, Canada
*
Author to whom correspondence should be addressed.
AppliedMath 2024, 4(1), 363-382; https://doi.org/10.3390/appliedmath4010019
Submission received: 16 January 2024 / Revised: 9 February 2024 / Accepted: 22 February 2024 / Published: 2 March 2024
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Abstract

Four measures of association, namely, Spearman’s ρ, Kendall’s τ, Blomqvist’s β and Hoeffding’s Φ2, are expressed in terms of copulas. Conveniently, this article also includes explicit expressions for their empirical counterparts. Moreover, copula representations of the four coefficients are provided for the multivariate case, and several specific applications are pointed out. Additionally, a numerical study is presented with a view to illustrating the types of relationships that each of the measures of association can detect.
Keywords: Blomqvist’s correlation coefficient; copulas; Hoeffding’s dependence index; Kendall’s rank correlation coefficient; multivariate measures of dependence; Spearman’s rank correlation Blomqvist’s correlation coefficient; copulas; Hoeffding’s dependence index; Kendall’s rank correlation coefficient; multivariate measures of dependence; Spearman’s rank correlation

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MDPI and ACS Style

Adès, M.; Provost, S.B.; Zang, Y. Four Measures of Association and Their Representations in Terms of Copulas. AppliedMath 2024, 4, 363-382. https://doi.org/10.3390/appliedmath4010019

AMA Style

Adès M, Provost SB, Zang Y. Four Measures of Association and Their Representations in Terms of Copulas. AppliedMath. 2024; 4(1):363-382. https://doi.org/10.3390/appliedmath4010019

Chicago/Turabian Style

Adès, Michel, Serge B. Provost, and Yishan Zang. 2024. "Four Measures of Association and Their Representations in Terms of Copulas" AppliedMath 4, no. 1: 363-382. https://doi.org/10.3390/appliedmath4010019

APA Style

Adès, M., Provost, S. B., & Zang, Y. (2024). Four Measures of Association and Their Representations in Terms of Copulas. AppliedMath, 4(1), 363-382. https://doi.org/10.3390/appliedmath4010019

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