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Title: Basic bounds of Fréchet classes (English)
Author: Skřivánek, Jaroslav
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 50
Issue: 1
Year: 2014
Pages: 95-108
Summary lang: English
Category: math
Summary: Algebraic bounds of Fréchet classes of copulas can be derived from the fundamental attributes of the associated copulas. A minimal system of algebraic bounds and related basic bounds can be defined using properties of pointed convex polyhedral cones and their relationship with non-negative solutions of systems of linear homogeneous Diophantine equations, largely studied in Combinatorics. The basic bounds are an algebraic improving of the Fréchet-Hoeffding bounds. We provide conditions of compatibility and propose tools for an explicit description of the basic bounds of simple Fréchet classes. (English)
Keyword: algebraic bound
Keyword: basic bound
Keyword: copula
Keyword: Diophantine equation
Keyword: Fréchet class
Keyword: pointed convex polyhedral cone
MSC: 11D75
MSC: 60E05
MSC: 62H20
idZBL: Zbl 1291.60034
idMR: MR3195006
DOI: 10.14736/kyb-2014-1-0095
Date available: 2014-05-02T06:48:07Z
Last updated: 2016-01-03
Stable URL:
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