Zonoids, Linear Dependence, and Size-Biased Distributions on the Simplex

Marco Scarsini and Marco Dall'Aglio

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Abstract: 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.

Keywords: Zonoid; zonotope; linear dependence; compositional variables; multivariate size-biased distribution; concordance order; Marshall-Olkin distribution (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (5)

Published in Advances in Applied Probability, 2003, Vol. 34, N°4, pp. 871-884. ⟨10.1239/aap/1067436324⟩

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Working Paper: Zonoids, Linear Dependence, and Size-Biased Distributions on the Simplex (2003)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00539799

DOI: 10.1239/aap/1067436324

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