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Relation between non-exchangeability and measures of concordance of copulas. (English) Zbl 1432.62151

Summary: 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.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H20 Measures of association (correlation, canonical correlation, etc.)
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