Relation between Blomqvist's beta and other measures of concordance of copulas

TL;DR

This paper explores the relationships between Blomqvist's beta and other key measures of concordance for copulas, introducing a novel estimation method to aid practitioners in selecting appropriate copulas for their data.

Contribution

It presents a new method for estimating four measures of concordance on copulas with fixed Blomqvist's beta, bridging gaps between these measures.

Findings

Established relationships between Blomqvist's beta and other concordance measures

Developed a novel estimation technique for copulas with fixed beta

Aimed at improving copula selection in practical data analysis

Abstract

An investigation is presented of how a comprehensive choice of four most important measures of concordance (namely Spearman's rho, Kendall's tau, Spearman's footrule, and Gini's gamma) relate to the fifth one, i.e., the Blomqvist's beta. In order to work out these results we present a novel method of estimating the values of the four measures of concordance on a family of copulas with fixed value of beta. These results are primarily aimed at the community of practitioners trying to find the right copula to be employed on their data. However, the proposed method as such may be of independent interest from theoretical point of view.