International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2004 / Article

Open Access

Volume 2004 |Article ID 593802 | https://doi.org/10.1155/S016117120440355X

H. H. Edwards, P. Mikusiński, M. D. Taylor, "Measures of concordance determined by -invariant copulas", International Journal of Mathematics and Mathematical Sciences, vol. 2004, Article ID 593802, 9 pages, 2004. https://doi.org/10.1155/S016117120440355X

Measures of concordance determined by D4-invariant copulas

Received25 Mar 2004

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.

Copyright © 2004 Hindawi Publishing Corporation. 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.


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