%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