Measures of concordance determined by \(D_4\)-invariant copulas
Summary: A continuous random vector \((X,Y)\) uniquely determines a copula \(C:[0,1]^2 \rightarrow [0,1]\) 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 \(D_4\)-invariant if its mass distribution is invariant with respect to the symmetries of the unit square. A \(D_4\)-invariant copula leads naturally to a family of measures of concordance having a particular form, and all copulas generating this family are \(D_4\)-invariant. The construction examined here includes Spearman's rho and Gini's measure of association as special cases.
scientific article; zbMATH DE number 2171827