1. Freedom in constructing quasi-copulas vs. copulasMatjaž Omladič, Nik Stopar, 2025, izvirni znanstveni članek Povzetek: The main goal of this paper is to study the extent of freedom one has in constructing quasi-copulas vs. copulas. Specifically, it exhibits three construction methods for quasi-copulas based on recent developments: a representation of multivariate quasi-copulas by means of infima and suprema of copulas, an extension of a classical result on shuffles of min to the setting of quasi-copulas, and a construction method for quasi-copulas obeying a given signed mass pattern on a patch.
Ključne besede: copulas, quasi-copulas, shuffles of min, patch, lattices
Objavljeno v DiRROS: 09.04.2025; Ogledov: 127; Prenosov: 51
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2. Extending multivariate sub-quasi-copulasDamjana Kokol-Bukovšek, Tomaž Košir, Blaž Mojškerc, Matjaž Omladič, 2024, izvirni znanstveni članek Povzetek: 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.
Ključne besede: mathematics, multivariate analysis
Objavljeno v DiRROS: 18.06.2024; Ogledov: 575; Prenosov: 326
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3. Coherence and avoidance of sure loss for standardized functions and semicopulasErich Peter Klement, Damjana Kokol-Bukovšek, Blaž Mojškerc, Matjaž Omladič, Susanne Saminger, Nik Stopar, 2024, izvirni znanstveni članek Povzetek: 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 $A \le C \le B$.
Ključne besede: copulas, quasi-copulas, semicopulas, standardized function, coherence, avoidance of sure loss, k-increasing function
Objavljeno v DiRROS: 13.03.2024; Ogledov: 666; Prenosov: 336
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