Measures of concordance determined by D 4 -invariant copulas

H. H. Edwards, P. Mikusiński and M. D. Taylor

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-9

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 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.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:593802

DOI: 10.1155/S016117120440355X

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