It is well known that every bivariate copula induces a positive measure on the Borel σ-algebra on 0,12, but there exist bivariate quasi-copulas that do not induce a signed measure on the same ...σ-algebra. In this paper we show that a signed measure induced by a bivariate quasi-copula can always be expressed as an infinite combination of measures induced by copulas. With this we are able to give the first characterization of measure-inducing quasi-copulas in the bivariate setting.
We correct the formula for the best-possible upper bound on the set of copulas with a given value of the Spearman's footrule coefficient recently published in 1.
In this paper, we introduce patchwork constructions for multivariate quasi-copulas. These results appear to be new since the kind of approach has been limited to either copulas or only bivariate ...quasi-copulas so far. It seems that the multivariate case is much more involved, since we are able to prove that some of the known methods of bivariate constructions cannot be extended to higher dimensions. Our main result is to present the necessary and sufficient conditions both on the patch and the values of it for the desired multivariate quasi-copula to exist. We also give all possible solutions.
Curved splicing of copulas Jwaid, T.; Meyer, H. De; Ismail, A. Haj ...
Information sciences,
20/May , Volume:
556
Journal Article
Peer reviewed
First, we recall the properties of the curved section of a copula that is specified by an automorphism of the unit interval. Then, inspired by the operation of diagonal splicing of two copulas, we ...develop the curved splicing operation, which essentially glues together different restrictions of two copulas that share the same curved section. In order to exploit this operation in practice, we propose two new classes of semilinear copulas. Applying the curved splicing operation to members of these two classes leads to two other classes of semilinear copulas.
Basic uncertain information (BUI) in the form <inline-formula><tex-math notation="LaTeX">\langle x;c \rangle </tex-math></inline-formula>, where <inline-formula><tex-math notation="LaTeX">x \in ...0,1</tex-math></inline-formula> is an observed datum and <inline-formula><tex-math notation="LaTeX">c \in 0,1</tex-math></inline-formula> is its reliability, is discussed and studied. The concept of BUI's aggregation is introduced and some construction methods are proposed and exemplified. The connection with interval-valued data and their aggregation is also discussed.
Our starting point are several general classes of real functions defined on the unit square satisfying some basic properties such as a boundary condition or several types of monotonicity and ...continuity. Applying to these functions some parameterized transformations and other constructions such as the transpose and flipping (which describe different aspects of symmetry) and truncation, we ask for conditions yielding (again) a bivariate copula. Some of these transformations are involutive (on one or more classes of functions), others are not even injective, and occasionally they induce additional properties, yielding, e.g., a (quasi-)copula. For several typical scenarios we identify the (not necessarily convex) sets of parameters leading to a copula and conditions imposing a minimal set of parameters.
Extending sub-quasi-copulas Kokol Bukovšek, Damjana; Košir, Tomaž; Omladič, Matjaž ...
Journal of mathematical analysis and applications,
08/2021, Volume:
500, Issue:
1
Journal Article
Peer reviewed
The main result of this paper is a method that gives all possible quasi-copulas that extend a given sub-quasi-copula to the whole domain, i.e., unit square 0,1×0,1. It is known that extending ...quasi-copulas is a deeper challenge than extending copulas, so we need to develop new techniques to do that. Perhaps surprisingly, our method is at the same time elementary and universal – two seemingly contradicting properties that none of the known methods for extending copulas seem to possesses. We also give a construction of two quasi-copulas that unveil an interesting counterexample in imprecise probability theory.
In this note we study the extremes of the mass distribution associated with a tetravariate quasi-copula and compare our results with the bi- and trivariate cases, showing the important differences ...between them.
Supports of quasi-copulas Fernández-Sánchez, Juan; Quesada-Molina, José Juan; Úbeda-Flores, Manuel
Fuzzy sets and systems,
09/2023, Volume:
467
Journal Article
Peer reviewed
Open access
It is known that for every s∈1,2 there is a copula whose support is a self-similar fractal set with Hausdorff —and box-counting— dimension s. In this paper we provide similar results for (proper) ...quasi-copulas, in both the bivariate and multivariate cases.
