Relation between non-exchangeability and measures of concordance of copulas
Damjana Kokol Bukov\v{s}ek, Toma\v{z} Ko\v{s}ir, Bla\v{z}, Moj\v{s}kerc, and Matja\v{z} Omladi\v{c}
TL;DR
This paper explores how various measures of concordance relate to non-exchangeability in copulas, introducing a new method for analyzing the dependence structure and asymmetry.
Contribution
It provides a comprehensive analysis of five key concordance measures in relation to copula asymmetry and proposes a novel method for exploring these relationships.
Findings
Identifies correlations between measures of concordance and non-exchangeability
Introduces a new method for analyzing dependence structures in copulas
Suggests potential for further exploration of dependence measures
Abstract
An investigation is presented of how a comprehensive choice of five most important measures of concordance (namely Spearman's rho, Kendall's tau, Gini's gamma, Blomqvist's beta, and their weaker counterpart Spearman's footrule) relate to non-exchangeability, i.e., asymmetry on copulas. Besides these results, the method proposed also seems to be new and may serve as a raw model for exploration of the relationship between a specific property of a copula and some of its measures of dependence structure, or perhaps the relationship between various measures of dependence structure themselves.
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