In this paper we study in detail the associativity property of the discrete copulas. We observe the connection between discrete copulas and the empirical copulas, and then we propose a statistic that indicates when an empirical copula is associative and obtain its main statistical properties under independence. We also obtained asymptotic results of the proposed statistic. Finally, we study the associativity statistic under different copulas and we include some final remarks about associativity of samples.
In this paper we analyze some properties of the discrete copulas in terms of permutations. We observe the connection between discrete copulas and the empirical copulas, and then we analyze a statistic that indicates when the discrete copula is symmetric and obtain its main statistical properties under independence. The results obtained are useful in designing a nonparametric test for symmetry of copulas.