Title

Characterizations of degree one bivariate measures of concordance

Authors

Authors

H. H. Edwards;M. D. Taylor

Comments

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Abbreviated Journal Title

J. Multivar. Anal.

Keywords

Copula; Measure of association; Measure of concordance; Statistics & Probability

Abstract

We call a measure of concordance kappa of an ordered pair. (X, Y) of two continuous random variables a bivariate measure of concordance. This kappa may be considered to be a function kappa(C) of the copula C associated with. (X, Y). kappa is considered to be of degree n if, given any two copulas A and B, the value of their convex sum, kappa(tA + (1-t)B), is a polynomial in t of degree n. Examples of bivariate measures of concordance are Spearman's rho, Blomqvist's beta, Gini's measure of association, and Kendall's tau. The first three of these are of degree one, but Kendall's tau is of degree two. We exhibit three characterizations of bivariate measures of concordance of degree one. (C) 2009 Elsevier Inc. All rights reserved.

Journal Title

Journal of Multivariate Analysis

Volume

100

Issue/Number

8

Publication Date

1-1-2009

Document Type

Article

Language

English

First Page

1777

Last Page

1791

WOS Identifier

WOS:000266565200016

ISSN

0047-259X

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