Multivariate Gini indices
AbstractThe Gini index and the Gini mean difference of a univariate distribution are extended to measure the disparity of a general d-variate distribution. We propose and investigate two approaches, one based on the distance of the distribution from itself, the other on the volume of a convex set in (d + 1)- space, named the lift zonoid of the distribution. When d = 1, this volume equals the area between the usual Lorenz curve and the line of zero disparity, up to a scale factor. We get two definitions of the multivariate Gini index, which are different (when d > 1) but connected through the notion of the lift zonoid. Both notions inherit properties of the univariate Gini index, in particular, they are vector scale invariant, continuous, bounded by 0 and 1, and the bounds are sharp. They vanish if and only if the distribution is concentrated at one point. The indices have a ceteris paribus property and are consistent with multivariate extensions of the Lorenz order. Illustrations with data conclude the paper. --
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. 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.
Bibliographic InfoPaper provided by University of Cologne, Department for Economic and Social Statistics in its series Discussion Papers in Statistics and Econometrics with number 7/95.
Date of creation: 1995
Date of revision:
Contact details of provider:
Postal: Albertus Magnus Platz, 50923 Köln
Phone: 0221 / 470 5607
Fax: 0221 / 470 5179
Web page: http://www.wisostat.uni-koeln.de/Englisch/index_en.html
More information through EDIRC
Dilation; Disparity measurement; Gini mean difference; Lift zonoid; Lorenz order;
Other versions of this item:
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Thibault Gajdos & John A. Weymark, 2003.
"Multidimensional generalized Gini indices,"
ICER Working Papers - Applied Mathematics Series
16-2003, ICER - International Centre for Economic Research.
- Thibault Gadjos & John A, Weymark, 2003. "Multidimensional Generalized Gini Indices," Working Papers 2003-16, Centre de Recherche en Economie et Statistique.
- Thibault Gajdos & John A. Weymark, 2003. "Multidimensional Generalized Gini Indices," Vanderbilt University Department of Economics Working Papers 0311, Vanderbilt University Department of Economics, revised Jul 2003.
- Thibault Gajdos & John Weymark, 2005. "Multidimensional Generalized Gini Indices," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00085881, HAL.
- 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.
- Chiara Gigliarano & Karl Mosler, 2009. "Constructing indices of multivariate polarization," Journal of Economic Inequality, Springer, vol. 7(4), pages 435-460, December.
- Karl Mosler, 2004.
"Restricted Lorenz dominance of economic inequality in one and many dimensions,"
Journal of Economic Inequality,
Springer, vol. 2(2), pages 89-103, August.
- 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.
- Anderson, Gordon, 2011. "Polarization measurement and inference in many dimensions when subgroups can not be identified," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy, vol. 5(11), pages 1-19.
- K. Mosler, 2003. "Central regions and dependency," Econometrics 0309004, EconWPA.
- Henar Diez & Mª Casilda Lasso de la Vega & Ana Marta Urrutia, 2007. "Unit-Consistent Aggregative Multidimensional Inequality Measures: A Characterization," Working Papers 66, ECINEQ, Society for the Study of Economic Inequality.
- Masato Okamoto, 2009. "Decomposition of gini and multivariate gini indices," Journal of Economic Inequality, Springer, vol. 7(2), pages 153-177, June.
- John A. Weymark, 2003. "The Normative Approach to the Measurement of Multidimensional Inequality," Vanderbilt University Department of Economics Working Papers 0314, Vanderbilt University Department of Economics, revised Jan 2004.
- Chiara GIGLIARANO & Karl MOSLER, 2009. "Measuring middle-class decline in one and many attributes," Working Papers 333, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
- E. Abdul-Sathar & R. Suresh & K. Nair, 2007. "A vector valued bivariate gini index for truncated distributions," Statistical Papers, Springer, vol. 48(4), pages 543-557, October.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (ZBW - German National Library of Economics).
If references are entirely missing, you can add them using this form.