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Intervals of 1-Lipschitz aggregation operators, quasi-copulas, and copulas with given affine section. (English) Zbl 1138.60016

Summary: Best lower and upper bounds for 1-Lipschitz aggregation operators with a given affine section are given. These are used to determine best bounds for quasi-copulas and copulas with a given affine section. However, in general there is no greatest copula with a given non-decreasing affine section. These results are used to study (quasi-)copulas with arbitrary affine sections.

MSC:

60E05 Probability distributions: general theory
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[11] Klement EP, Kolesárová A, Mesiar R, Sempi C (2007) Copulas constructed from horizontal sections. Commun Stat Theory Methods 36: in press · Zbl 1130.60017
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[15] Nelsen RB (1999) An Introduction to Copulas. Lect Notes Statistics 139. New York: Springer · Zbl 0909.62052
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