Kybernetika 46 no. 1, 149-177, 2010

Statistical aspects of associativity for copulas

José M. González–Barrios


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.


independence, discrete copulas, associativity, permutations


60C05, 62E15, 62H05