New asymmetric perturbations of FGM bivariate copulas and concordance preserving problems

El maazouz, Mohamed; Sani, Ahmed

doi:10.2478/mjpaa-2023-0008

Abstract

New copulas, based on perturbation theory, are introduced to clarify a symmetrization procedure for asymmetric copulas. We give also some properties of the symmetrized copula mainly conservation of concordance. Finally, we examine some copulas with a prescribed symmetrized part. The start point of the treatment is the independence copula and the last one will be an arbitrary member of Farlie-Gumbel-Morgenstein family. By the way, we study topologically, the set of all symmetric copulas and give some of its classical and new properties.

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New asymmetric perturbations of FGM bivariate copulas and concordance preserving problems

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