Bivariate quadratic transformations of quasi-copulas

Abstract

In this dissertation, we focus on bivariate quadratic transformations of trivariate quasi-copulas which are in the form of compositions between a quadratic polynomial and two quasi-copulas. The class of these transformations is characterized for necessary and sufficient conditions. The obtained conditions only depend on coefficients of the quadratic polynomial. Furthermore, the class of these coefficients forms a convex set with linear-section boundary in the seven-dimensional Euclidean space. All extreme points of this class are provided via a computer algebra system. They are used to construct our transformations. Construction examples are also presented.