Copula-based Berkson measurement error models

In this work, we consider the joint distribution function as well as the copula of $(X+Z,Y)$ where the random vector $(X, Y, Z)$  is characterized by a copula $C_{X,Y,Z}$. We use this copula to analyze a Berkson measurement error model. By presenting a general form of a Berkson measurement error model with copula-dependent random variables, we investigate some of its special cases. Some theoretical results, several examples as well as a simulation study, are proposed for illustration.