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Bivariate copulas: Transformations, asymmetry and measures of concordance

Bivariate copulas: Transformations, asymmetry and measures of concordance

The present paper introduces a group of transformations on the collection of all bivariate copulas.This group contains an involution which is particularly useful since it provides (1) a criterion under which a given symmetric copula can be transformed into an asymmetric one and (2) a condition under which for a …