International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 69-72, Pages 3867-3875
doi:10.1155/S016117120440355X
Measures of concordance determined by D4-invariant copulas
H.H. Edwards
, P. Mikusiński
and M.D. Taylor
Department of Mathematics, University of Central Florida, Orlando 32816-1364, FL, USA
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.