Diversity of Bivariate Concordance Measures

We revisit the axioms of Scarsini, defining bivariate concordance measures for a pair continuous random variables (X,Y); such can be understood as functions copula C associated with (X,Y). Two constructions, investigated in works Edwards, Mikusiński, Taylor, and Fuchs, are generalized, yielding, particular, examples higher than degree-two polynomial-type measures, along non-polynomial-type providing an incentive to investigate possible further characterizations was achieved by Edwards Taylor degree-one case.