In this paper, we address the concept of conditional independence between two random variables X and Y given the entity Θ. We identify the impact of conditional independence on the analytic form of the predictive 2-copula between X and Y. We obtain a representation of the predictive 2-copula between X and Y in terms of functions associated with the copulas between X and Θ and between Y and Θ. Through the concept of infinite exchangeable sequences we amplify the validity of our results, obtaining the predictive 2-copula between two variables in terms of the copula between only one of these variables and the quantity Θ.

In this paper, we introduce a method to construct copulas. The method is based on combining the partial derivatives of two copulas. We prove that the proposed method provides a copula. Then, we exemplify the application of the method in several cases, illustrating the versatility of the method. We also prove that using copulas from the family introduced in Rodríguez-Lallena and Úbeda-Flores (2004) [Stat Probab Lett 66, 3, 315–325. https://doi.org/10.1016/j.spl.2003.09.010], the method provides a copula inside that family.