This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

Multivariate Gini Indices

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
Koshevoy, G. A.
Mosler, K.

Additional information is available for the following registered author(s):

Abstract

Two extensions of the univariate Gini index are considered:RD, based on expected distance between two independent vectors from the same distribution with finite mean[mu][set membership, variant]d; andRV, related to the expected volume of the simplex formed fromd+1 independent such vectors. A new characterization ofRDas proportional to a univariate Gini index for a particular linear combination of attributes relates it to the Lorenz zonoid. TheLorenz zonoidwas suggested as a multivariate generalization of the Lorenz curve.RVis, up to scaling, the volume of the Lorenz zonoid plus a unit cube of full dimension. Whend=1, bothRDandRVequal twice the area between the usual Lorenz curve and the line of zero disparity. Whend>1, they are different, but inherit properties of the univariate Gini index and are related via the Lorenz zonoid:RDis proportional to the average of the areas of some two-dimensioned projections of the lift zonoid, whileRVis the average of the volumes of projections of the Lorenz zonoid over all coordinate subspaces.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.sciencedirect.com/science/article/B6WK9-45K12XT-G/2/ebcd2589d29fd988f3a60fff49fe38f3
File Format:
File Function:
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Publisher Info
Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 60 (1997)
Issue (Month): 2 (February)
Pages: 252-276
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Handle: RePEc:eee:jmvana:v:60:y:1997:i:2:p:252-276

Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description

Order Information:
Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
Web: https://shop.elsevier.com/order?id=622892&ref=622892_01_ooc_1&version=01

For technical questions regarding this item, or to correct its listing, contact: (Heidi Boesdal).

Related research
Keywords: dilation disparity measurement Gini mean difference lift zonoid Lorenz order;

Other versions of this item:

References listed on IDEAS
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.:
  1. Oja, Hannu, 1983. "Descriptive statistics for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 327-332, October. [Downloadable!] (restricted)
  2. Giovanni Maria Giorgi, 2005. "Bibliographic portrait of the Gini concentration ratio," Econometrics 0511004, EconWPA. [Downloadable!]
  3. Giovagnoli, Alessandra & Wynn, H. P., 1995. "Multivariate dispersion orderings," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 325-332, March. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, 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.)

  1. John A. Weymark, 2003. "The Normative Approach to the Measurement of Multidimensional Inequality," Working Papers 0314, Department of Economics, Vanderbilt University, revised Jan 2004. [Downloadable!]
  2. Masato Okamoto, 2009. "Decomposition of gini and multivariate gini indices," Journal of Economic Inequality, Springer, vol. 7(2), pages 153-177, June. [Downloadable!] (restricted)
  3. K. Mosler, 2003. "Central regions and dependency," Econometrics 0309004, EconWPA. [Downloadable!]
  4. Gordon Anderson, 2008. "The empirical assessment of multidimensional welfare, inequality and poverty: Sample weighted multivariate generalizations of the Kolmogorov–Smirnov two sample tests for stochastic dominance," Journal of Economic Inequality, Springer, vol. 6(1), pages 73-87, March. [Downloadable!] (restricted)
  5. Marco Dall’Aglio & Marco Scarsini, 2000. "Zonoids, Linear Dependence, and Size-Biased Distributions on the Simplex," ICER Working Papers - Applied Mathematics Series 27-2003, ICER - International Centre for Economic Research, revised Jul 2003. [Downloadable!]
  6. Thibault Gajdos & John Weymark, 2005. "Multidimensional Generalized Gini Indices," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00085881_v1, HAL. [Downloadable!]
    Other versions:
  7. Karl Mosler, 2005. "Restricted Lorenz dominance of economic inequality in one and many dimensions," Journal of Economic Inequality, Springer, vol. 2(2), pages 89-103, January. [Downloadable!] (restricted)
    Other versions:
Statistics
Access and download statistics

Did you know? IDEAS also indexes book chapters.

This page was last updated on 2009-11-7.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.