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...
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].
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.
In this paper we analyze the construction of -copulas including the ideas of Cuculescu and Theodorescu [5], Fredricks et al. [15], Mikusiński and Taylor [25] and Trutschnig and Fernández-Sánchez [33]. Some of these methods use iterative procedures to construct copulas with fractal supports. The main part of this paper is given in Section 3, where we introduce the sample -copula of order with , the central idea is to use the above methodologies to construct a new copula based on a sample. The...
In this paper we give an alternative proof of the construction of -dimensional ordinal sums given in Mesiar and Sempi [17], we also provide a new methodology to construct -copulas extending the patchwork methodology of Durante, Saminger-Platz and Sarkoci in [6] and [7]. Finally, we use the gluing method of Siburg and Stoimenov [20] and its generalization in Mesiar et al. [15] to give an alternative method of patchwork construction of -copulas, which can be also used in composition with our patchwork...
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