标题：Measures of concordance determined by <mml:math alttext="$D_4$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>D</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:math>-invariant copulas
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2004
卷号：2004
DOI：10.1155/S016117120440355X
出版社：Hindawi Publishing Corporation
摘要：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.
