New results on discrete copulas and quasi-copulas

In this paper we prove that the set of all irreducible discrete quasi-copulas coincides with the set of all discrete quasi-copulas with minimal range. We also provide answers, throughout some counterexamples, to two questions posed in Aguil & oacute; et al. [2] regarding both discrete quasi-copulas with minimal range and irreducible discrete quasi-copulas. Some additional results concerning discrete (quasi-)copulas are also given. (c) 2020 Elsevier B.V. All rights reserved.

Automated summary

This paper proves the equivalence between the set of all irreducible discrete quasi-copulas and the set of all discrete quasi-copulas with minimal range. It also provides answers to questions posed in previous literature and offers additional results on discrete (quasi-)copulas.