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.

翻译：通过研究洗牌（shuffles），我们建立了Kendall's tau、所谓的长度测度（length measure）以及二元Copula表面积之间的紧密联系，并推导出若干推论。众所周知，二元Copula A的Spearman's rho是A图形下方面积的缩放版本，而本文则表明另一著名的和谐性度量——Kendall's tau——同样具有简单的几何解释：它与A的表面积存在不可分割的联系。