Copula and semicopula transforms.
Las métricas de Orlicz derivan de una única métrica probabilística.
It is shown that the same probabilistic metric as used by Schweizer and Sklar to obtain all L space metrics can be used to derive the metrics of Orlicz spaces.
The space of distribution functions is separable.
The space of distribution functions endowed with the metric introduced in [5] is separable.
Completion of probabilistic normed spaces.
Pruning and measures of uncertainty
A remark on metrics for finitely additive distribution functions.
Semicopulæ
We define the notion of semicopula, a concept that has already appeared in the statistical literature and study the properties of semicopulas and the connexion of this notion with those of copula, quasi-copula, -norm.
Editorial to the special issue on “Random Variables, Joint Distribution Functions, and Copulas”
Semicopulas: characterizations and applicability
We characterize some bivariate semicopulas and, among them, the semicopulas satisfying a Lipschitz condition. In particular, the characterization of harmonic semicopulas allows us to introduce a new concept of depedence between two random variables. The notion of multivariate semicopula is given and two applications in the theory of fuzzy measures and stochastic processes are given.
Copulas with given values on a horizontal and a vertical section
In this paper we study the set of copulas for which both a horizontal section and a vertical section have been given. We give a general construction for copulas of this type and we provide the lower and upper copulas with these sections. Symmetric copulas with given horizontal section are also discussed, as well as copulas defined on a grid of the unit square. Several examples are presented.
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