%0 Journal Article
%T Zonoids, Linear Dependence, and Size-Biased Distributions on the Simplex
%+ Groupement de Recherche et d'Etudes en Gestion à HEC (GREGH)
%+ Dipartimento di Scienze Economiche e Aziendali
%A Scarsini, Marco
%A Dall'Aglio, Marco
%< avec comité de lecture
%@ 0001-8678
%J Advances in Applied Probability
%I Applied Probability Trust
%V Vol. 34, N°4
%P pp. 871-884
%8 2003
%D 2003
%R 10.1239/aap/1067436324
%K Zonoid
%K zonotope
%K linear dependence
%K compositional variables
%K multivariate size-biased distribution
%K concordance order
%K Marshall-Olkin distribution
%Z Humanities and Social Sciences/Economics and Finance/domain_shs.eco.ecoJournal articles
%X The zonoid of a d-dimensional random vector is used as a tool for measuring linear dependence among its components. A preorder of linear dependence is defined through inclusion of the zonoids. The zonoid of a random vector does not characterize its distribution, but it does characterize the size-biased distribution of its compositional variables. This fact will allow a characterization of our linear dependence order in terms of a linear-convex order for the size-biased compositional variables. In dimension 2 the linear dependence preorder will be shown to be weaker than the concordance order. Some examples related to the Marshall-Olkin distribution and to a copula model will be presented, and a class of measures of linear dependence will be proposed.
%G English
%L hal-00539799
%U https://hec.hal.science/hal-00539799
%~ SHS
%~ HEC
%~ CNRS
%~ AO-ECONOMIE