Multivariate Gini indices

Gleb Koshevoy and Karl Mosler

No 7/95, Discussion Papers in Econometrics and Statistics from University of Cologne, Institute of Econometrics and Statistics

Abstract: The 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.

Keywords: Dilation; Disparity measurement; Gini mean difference; Lift zonoid; Lorenz order (search for similar items in EconPapers)
Date: 1995
References: Add references at CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://www.econstor.eu/bitstream/10419/45473/1/657506087.pdf (application/pdf)

Related works:
Journal Article: Multivariate Gini Indices (1997)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:zbw:ucdpse:9507

Access Statistics for this paper

More papers in Discussion Papers in Econometrics and Statistics from University of Cologne, Institute of Econometrics and Statistics Contact information at EDIRC.
Bibliographic data for series maintained by ZBW - Leibniz Information Centre for Economics ().