In this paper we analyze some properties of the empirical diagonal and we obtain its exact distribution under independence for the two and three-dimensional cases, but the ideas proposed in this paper can be carried out to higher dimensions. The results obtained are useful in designing a nonparametric test for independence, and therefore giving solution to an open problem proposed by Alsina, Frank and Schweizer [2].
Several constructions of additive generators of binary Archimedean copulas are introduced and discussed. Extension to general Archimedean copulas is also included. Applications to the fitting of copulas to real data are given and examplified.