Polynomial copula transformations

Abstract

© 2019 Elsevier Inc. In this study, we demonstrate that the problem of characterizing polynomial copula transformations can be reduced to solving a system of (in)equalities. In this case, no knowledge of copulas is necessary to find an instance of such polynomials, or even the whole set of such polynomials. As a demonstration, we employ this result to characterize all quadratic polynomials that define copula transformations.