International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 70, Pages 3867-3875
doi:10.1155/S016117120440355X
Measures of concordance determined by D4-invariant copulas
Department of Mathematics, University of Central Florida, Orlando 32816-1364, FL, USA
Received 25 March 2004
Copyright © 2004 H. H. Edwards et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.