Measures of concordance determined by \(D_4\)-invariant copulas
type: Item
instance of: scholarly article
title: Measures of concordance determined by \(D_4\)-invariant copulas
zbMATH Open document ID: 1075.62042
DOI: 10.1155/S016117120440355X
author: H. H. Edwards
author: Piotr Mikusiński
author: Michael Taylor
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-25T00:00:00Z
full work available at URL: https://eudml.org/doc/51798
review text: Summary: A continuous random vector \((X,Y)\) uniquely determines a copula \(C:[0,1]^2 \rightarrow [0,1]\) 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.
Mathematics Subject Classification ID: 62H05
Mathematics Subject Classification ID: 62H20
zbMATH DE Number: 2171827
MaRDI profile type: Publication
OpenAlex ID: W1995284392
description: scientific article; zbMATH DE number 2171827