Abstract
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.