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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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|
|Date Deposited:||22 Nov 2010 12:34|
|Last Modified:||22 Apr 2015 00:13|
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