Displaying similar documents to “Remarks on Two Product-like Constructions for Copulas”

Asymmetric semilinear copulas

Bernard De Baets, Hans De Meyer, Radko Mesiar (2007)

Kybernetika

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We complement the recently introduced classes of lower and upper semilinear copulas by two new classes, called vertical and horizontal semilinear copulas, and characterize the corresponding class of diagonals. The new copulas are in essence asymmetric, with maximum asymmetry given by 1 / 16 . The only symmetric members turn out to be also lower and upper semilinear copulas, namely convex sums of Π and M .

A new family of trivariate proper quasi-copulas

Manuel Úbeda-Flores (2007)

Kybernetika

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In this paper, we provide a new family of trivariate proper quasi-copulas. As an application, we show that W 3 – the best-possible lower bound for the set of trivariate quasi-copulas (and copulas) – is the limit member of this family, showing how the mass of W 3 is distributed on the plane x + y + z = 2 of [ 0 , 1 ] 3 in an easy manner, and providing the generalization of this result to n dimensions.

On possibilistic marginal problem

Jiřina Vejnarová (2007)

Kybernetika

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A possibilistic marginal problem is introduced in a way analogous to probabilistic framework, to address the question of whether or not a common extension exists for a given set of marginal distributions. Similarities and differences between possibilistic and probabilistic marginal problems will be demonstrated, concerning necessary condition and sets of all solutions. The operators of composition will be recalled and we will show how to use them for finding a T -product extension. Finally,...

Copulas with given values on a horizontal and a vertical section

Fabrizio Durante, Anna Kolesárová, Radko Mesiar, Carlo Sempi (2007)

Kybernetika

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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.