Geodesic
Basic bounds of Fréchet classes
Kybernetika, Tome 50 (2014) no. 1, pp. 95-108 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.14736/kyb-2014-1-0095
Classification : 11D75, 60E05, 62H20
Keywords: algebraic bound; basic bound; copula; Diophantine equation; Fréchet class; pointed convex polyhedral cone 
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     title = {Basic bounds of {Fr\'echet} classes},
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     pages = {95--108},
     year = {2014},
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     zbl = {1291.60034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-1-0095/}
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Skřivánek, Jaroslav. Basic bounds of Fréchet classes. Kybernetika, Tome 50 (2014) no. 1, pp. 95-108. doi: 10.14736/kyb-2014-1-0095

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