A link between Kendall’s τ, the length measure and the surface of bivariate copulas, and a consequence to copulas with self-similar support

Sánchez Juan Fernández () and Trutschnig Wolfgang ()
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Sánchez Juan Fernández: Grupo de Investigación de Análisis Matemático, Universidad de Almería, 04120 La Cañada de San Urbano, Almería, Spain
Trutschnig Wolfgang: Department for Artificial Intelligence & Human Interfaces, University of Salzburg, Hellbrunnerstrasse 34, 5020 Salzburg, Austria

Dependence Modeling, 2023, vol. 11, issue 1, 14

Abstract: Working with shuffles, we establish a close link between Kendall’s τ \tau , the so-called length measure, and the surface area of bivariate copulas and derive some consequences. While it is well known that Spearman’s ρ \rho of a bivariate copula A A is a rescaled version of the volume of the area under the graph of A A , in this contribution we show that the other famous concordance measure, Kendall’s τ \tau , allows for a simple geometric interpretation as well – it is inextricably linked to the surface area of A A .

Keywords: asymmetry; copula; dependence measure; exchangeability; Markov kernel (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:11:y:2023:i:1:p:14:n:1

DOI: 10.1515/demo-2023-0105

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