Kybernetika 50 no. 1, 95-108, 2014

Basic bounds of Fréchet classes

Jaroslav SkřivánekDOI: 10.14736/kyb-2014-1-0095

Abstract:

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.

Keywords:

copula, Fréchet class, Diophantine equation, algebraic bound, basic bound, pointed convex polyhedral cone

Classification:

60E05, 62H20, 11D75

paper.pdf

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