Zonoids, Linear Dependence, and Size-Biased Distributions on the Simplex
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.
|Date of creation:||Dec 2000|
|Date of revision:||Jul 2003|
|Contact details of provider:|| Postal: |
Phone: +39 011 6706060
Fax: +39 011 6706060
Web page: http://www.esomas.unito.it/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Dall'Aglio, Marco & Scarsini, Marco, 2001. "When Lorenz met Lyapunov," Statistics & Probability Letters, Elsevier, vol. 54(1), pages 101-105, August.
- Koshevoy, Gleb & Mosler, Karl, 1995.
"Multivariate Gini indices,"
Discussion Papers in Econometrics and Statistics
7/95, University of Cologne, Institute of Econometrics and Statistics.
- Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
- Gleb Koshevoy, 1997. "The Lorenz zonotope and multivariate majorizations," Social Choice and Welfare, Springer, vol. 15(1), pages 1-14.
- Machina, Mark J & Pratt, John W, 1997. "Increasing Risk: Some Direct Constructions," Journal of Risk and Uncertainty, Springer, vol. 14(2), pages 103-27, March.
- K. Mosler, 2003. "Central regions and dependency," Econometrics 0309004, EconWPA.
When requesting a correction, please mention this item's handle: RePEc:icr:wpmath:27-2003. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Simone Pellegrino)
If references are entirely missing, you can add them using this form.