Measures of concordance determined by D4-invariant copulas - H. H. Edwards; P. Mikusiński; M. D. Taylor (International Journal of Mathematics and Mathematical Sciences)
A continuous random vector (X,Y) uniquely determines a copula C:[0,1]2→[0,1] such that when the distribution functions of X and Y are properly composed into C, the joint distribution function of (X,Y) results. A copula is said to be D4-invariant if its mass distribution is invariant with respect to the symmetries of the unit square. A D4-invariant copula leads naturally to a family of measures of concordance having a particular form, and all copulas generating this family are D4-invariant. The construction examined here includes Spearman’s rho and Gini’s measure of association as special cases.