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

Dall'Aglio, Marco and Scarsini, Marco (2003) Zonoids, Linear Dependence, and Size-Biased Distributions on the Simplex. [Working Paper]. p. 25. ICER Working Papers - Applied Mathematics Series (no. 27/2003).

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Abstract/Index

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 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.


Item Type:Report / Paper (Working Paper)
Research documents and activity classification:Working Papers > Refereed Working Papers / of international relevance
Divisions:Department of Business and Management
Additional Information:The definitive version of this paper has been published in "Advances in Applied Probability", Vol. 35 (2003), n.4, 871-884, ISSN 0001-8678.
Uncontrolled Keywords:Zonoid, Zonotope, Linear Dependence, Compositional Variables, Multivariate Size Biased Distribution, Concordance Order, Marshall-Olkin Distribution.
MIUR Scientific Area:Area 13 - Economics and Statistics > SECS-S/06 Mathematics for Economics, Actuarial Studies and Finance
Deposited By:Maria Teresa Nistico
Deposited On:22 Nov 2010 13:34
Last Modified:29 Nov 2010 20:04

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