Zonoids, Linear Dependence, and Size-Biased Distributions on the Simplex
AbstractThe 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 characterizes 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.
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Bibliographic InfoPaper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 27-2003.
Length: 25 pages
Date of creation: Dec 2000
Date of revision: Jul 2003
zonoid; zonotope; linear dependence; compositional variables; multivariate size biased distribution; concordance order; Marshall-Olkin distribution.;
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