Diversity of Bivariate Concordance Measures

Abstract

We revisit the axioms of Scarsini, defining bivariate concordance measures 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). Two constructions, investigated in the works of Edwards, Mikusiński, Taylor, and Fuchs, are generalized, yielding, in particular, examples of higher than degree-two polynomial-type concordance measures, along with examples of non-polynomial-type concordance measures, and providing an incentive to investigate possible further characterizations of such concordance measures, as was achieved by Edwards and Taylor for the degree-one case.

Keywords

• scarsini axioms
• bivariate copula
• transformation
• polynomial-type concordance measure
• multiplicative function