Multivariate Measures of Concordance for Copulas and their Marginals

TL;DR

This paper explores properties of multivariate measures of concordance for copulas, focusing on their relationships with marginal measures, advancing the theoretical understanding of dependence structures in multivariate distributions.

Contribution

It introduces new insights into how multivariate concordance measures relate to marginal measures, extending previous axiomatic frameworks.

Findings

Established relations between n-copula and marginal concordance measures

Extended axiomatic framework for multivariate concordance

Provided theoretical properties of concordance measures

Abstract

Building upon earlier work in which axioms were formulated for multivariate measures of concordance, we examine properties of such measures. In particular, we examine the relations between the measure of concordance of an $n$-copula and the measures of concordance of the copula's marginals.