On degrees of asymmetry of a copula with respect to a track

In this paper, we provide lower and upper bounds on the degree of asymmetry of a copula with respect to a track-a continuous and strictly increasing curve in the unit square-, generalizing the problem with respect to the main diagonal. We also study an average asymmetry in sections for given tracks. Finally, we also give an asymmetry map with respect to the opposite diagonal. (C) 2018 Elsevier B.V. All rights reserved.