Bivariate Quadratic Transformations of Quasi-copulas

Abstract

In this study, we construct a bivariate quadratic transformation of trivariate quasi-copulas. This construction yields new quasi-copulas by composing two priori given quasi-copulas with a quadratic polynomial function. We show that the constructed transformation is not a bivariate transformation of semi-copulas which show that these two classes of transformations are different. The constructed transformation is also not symmetric which implies similar transformations can be constructed via change of variables. This also implies that these transformations cannot be constructed from univariate transformations which show that the class of bivariate transformations is much larger and more complicated than that of the univariate case.