63 research outputs found
Distorted Copulas: Constructions and Tail Dependence
Given a copula C, we examine under which conditions on an order isomorphism ψ of [0, 1] the distortion C ψ: [0, 1]2 → [0, 1], C ψ(x, y) = ψ{C[ψ−1(x), ψ−1(y)]} is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on ψ that ensures that any distortion of C by means of ψ is again a copula. The presented results allow us to introduce in a more flexible way families of copulas exhibiting different behavior in the tails
Evolution of the Dependence of Residual Lifetimes
We investigate the dependence properties of a vector of residual lifetimes by means of the copula associated with the conditional distribution function. In particular, the evolution of positive dependence properties (like quadrant dependence and total positivity) are analyzed and expressions for the evolution of measures of association are given
Bivariate copulas defined from matrices
We propose a semiparametric family of copulas based on a set of orthonormal
functions and a matrix. This new copula permits to reach values of Spearman's
Rho arbitrarily close to one without introducing a singular component.
Moreover, it encompasses several extensions of FGM copulas as well as copulas
based on partition of unity such as Bernstein or checkerboard copulas. Finally,
it is also shown that projection of arbitrary densities of copulas onto tensor
product bases can enter our framework
Copulas in Hilbert spaces
In this article, the concept of copulas is generalised to infinite
dimensional Hilbert spaces. We show one direction of Sklar's theorem and
explain that the other direction fails in infinite dimensional Hilbert spaces.
We derive a necessary and sufficient condition which allows to state this
direction of Sklar's theorem in Hilbert spaces. We consider copulas with
densities and specifically construct copulas in a Hilbert space by a family of
pairwise copulas with densities
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