Title

Characterizations Of Degree One Bivariate Measures Of Concordance

Keywords

Copula; Measure of association; Measure of concordance

Abstract

We call a measure of concordance κ of an ordered pair (X, Y) of two continuous random variables a bivariate measure of concordance. This κ may be considered to be a function κ (C) of the copula C associated with (X, Y). κ is considered to be of degree n if, given any two copulas A and B, the value of their convex sum, κ (t A + (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. © 2009 Elsevier Inc. All rights reserved.

Publication Date

9-1-2009

Publication Title

Journal of Multivariate Analysis

Volume

100

Issue

8

Number of Pages

1777-1791

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jmva.2009.02.003

Socpus ID

67349134669 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/67349134669

This document is currently not available here.

Share

COinS