Description
Complimenting our earlier work (Manstavicius, M. Diversity of Bivariate Concordance Measures. Mathematics 2022, 10, 1103. https://doi.org/10.3390/math10071103) on generalizations of popular concordance measures in the sense of Scarsini for a pair of continuous random variables (X, Y) (such measures can be understood as functions of the bivariate copula C associated with (X, Y)), we focus on generalizations of Kendall’s tau.
We give two forms of such measures and also provide general bounds for their values, which are sharp in certain cases and depend on the values of Spearman’s rho and the original Kendall’s tau. Presented examples further illustrate the intrinsic meaning and influence of the distortion function used to construct such generalizations.