Bivariate quadratic copula constructions

摘要

In this study, we present the concept of quadratic copula constructions using two arbitrary copulas. We characterize all quadratic polynomials of four variables whose composition with any two copulas always results in a copula. We show that these polynomials form a compact convex set in a seven-dimensional vector space. We also apply the result to obtain a new family of copulas. (C) 2017 Elsevier Inc. All rights reserved.