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Query: "author" (Omladič Matjaž) .

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1.
Extending multivariate sub-quasi-copulas
Damjana Kokol-Bukovšek, Tomaž Košir, Blaž Mojškerc, Matjaž Omladič, 2024, original scientific article

Abstract: 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.
Keywords: mathematics, multivariate analysis
Published in DiRROS: 18.06.2024; Views: 55; Downloads: 35
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2.
Coherence and avoidance of sure loss for standardized functions and semicopulas
Erich Peter Klement, Damjana Kokol-Bukovšek, Blaž Mojškerc, Matjaž Omladič, Susanne Saminger, Nik Stopar, 2024, original scientific article

Abstract: We discuss avoidance of sure loss and coherence results for semicopulas and standardized functions, i.e., for grounded, $1$-increasing functions with value $1$ at $(1, 1, \ldots , 1)$. We characterize the existence of a $k$-increasing $n$-variate function $C$ fulfilling $A \le C \le B$ for standardized $n$-variate functions $A$, $B$ and discuss methods for constructing such functions. Our proofs also include procedures for extending functions on some countably infinite mesh to functions on the unit box. We provide a characterization when $A$ respectively $B$ coincides with the pointwise infimum respectively supremum of the set of all $k$-increasing $n$-variate functions $C$ fulfilling $A \le C \le B$.
Keywords: copulas, quasi-copulas, semicopulas, standardized function, coherence, avoidance of sure loss, k-increasing function
Published in DiRROS: 13.03.2024; Views: 192; Downloads: 100
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