Displaying similar documents to “On a problem by Schweizer and Sklar”

Construction of multivariate copulas in n -boxes

José M. González-Barrios, María M. Hernández-Cedillo (2013)

Kybernetika

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In this paper we give an alternative proof of the construction of n -dimensional ordinal sums given in Mesiar and Sempi [17], we also provide a new methodology to construct n -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 n -copulas, which can be also used in composition...

Constructing families of symmetric dependence functions

Włodzimierz Wysocki (2012)

Kybernetika

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We construct two pairs ( 𝒜 F [ 1 ] , 𝒜 F [ 2 ] ) and ( 𝒜 ψ [ 1 ] , 𝒜 ψ [ 2 ] ) of ordered parametric families of symmetric dependence functions. The families of the first pair are indexed by regular distribution functions F , and those of the second pair by elements ψ of a specific function family ψ . We also show that all solutions of the differential equation d y d u = α ( u ) u ( 1 - u ) y for α in a certain function family α s are symmetric dependence functions.

Bounds of general Fréchet classes

Jaroslav Skřivánek (2012)

Kybernetika

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This paper deals with conditions of compatibility of a system of copulas and with bounds of general Fréchet classes. Algebraic search for the bounds is interpreted as a solution to a linear system of Diophantine equations. Classical analytical specification of the bounds is described.

Multivariate copulas: Transformations, symmetry, order and measures of concordance

Sebastian Fuchs (2014)

Kybernetika

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The present paper introduces a group of transformations on the collection of all multivariate copulas. The group contains a subgroup which is of particular interest since its elements preserve symmetry, the concordance order between two copulas and the value of every measure of concordance.

Equivalence of compositional expressions and independence relations in compositional models

Francesco M. Malvestuto (2014)

Kybernetika

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We generalize Jiroušek’s (right) composition operator in such a way that it can be applied to distribution functions with values in a “semifield“, and introduce (parenthesized) compositional expressions, which in some sense generalize Jiroušek’s “generating sequences” of compositional models. We say that two compositional expressions are equivalent if their evaluations always produce the same results whenever they are defined. Our first result is that a set system ℋ is star-like with...