New copulas and their applications to symmetrizations of bivariate copulas
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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. Finally, we examine families of copulas with a prescribed symmetrized one. 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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