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

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