1. 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, 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: 88; Downloads: 54
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2. On the exact region determined by Spearman's rho and Spearman's footruleDamjana Kokol-Bukovšek, Nik Stopar, 2024, original scientific article Abstract: We determine the lower bound for possible values of Spearman’s rho of a bivariate copula given that the value of its Spearman's footrule is known and show that this bound is always attained. We also give an estimate for the exact upper bound and prove that the estimate is exact for some but not all values of Spearman's footrule. Nevertheless, we show that the estimate is quite tight.
Keywords: copula, dependence concepts, supremum and infimum of a set of copulas, measures of concordance, quasi-copula, local bounds
Published in DiRROS: 13.03.2024; Views: 105; Downloads: 61
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3. Quasi-copulas as linear combinations of copulasGregor Dolinar, Bojan Kuzma, Nik Stopar, 2024, original scientific article Abstract: We prove that every quasi-copula can be written as a uniformly converging infinite sum of multiples of copulas. Furthermore, we characterize those quasi-copulas which can be written as a finite sum of multiples of copulas, i.e., that are a linear combination of two copulas. This generalizes a recent result of Fernández-Sánchez, Quesada-Molina, and Úbeda-Flores who considered linear combinations of discrete copulas.
Keywords: quasi-copulas, copulas, linear combination, affine combination, Minkowski norm
Published in DiRROS: 16.02.2024; Views: 156; Downloads: 66
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