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

03/27/2023

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by   Juan Fernández-Sánchez, et al.

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Working with shuffles we establish a close link between Kendall's 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 rho of a bivariate copula A is a rescaled version of the volume of the area under the graph of A, in this contribution we show that the other famous concordance measure, Kendall's tau, allows for a simple geometric interpretation as well - it is inextricably linked to the surface area of A.