Arbeitspapier
Multivariate Gini indices
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.
- Language
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Englisch
- Bibliographic citation
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Series: Discussion Papers in Statistics and Econometrics ; No. 7/95
- Classification
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Wirtschaft
- Subject
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Dilation
Disparity measurement
Gini mean difference
Lift zonoid
Lorenz order
- Event
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Geistige Schöpfung
- (who)
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Koshevoy, Gleb
Mosler, Karl
- Event
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Veröffentlichung
- (who)
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University of Cologne, Seminar of Economic and Social Statistics
- (where)
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Cologne
- (when)
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1995
- Handle
- Last update
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10.03.2025, 11:43 AM CET
Data provider
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Object type
- Arbeitspapier
Associated
- Koshevoy, Gleb
- Mosler, Karl
- University of Cologne, Seminar of Economic and Social Statistics
Time of origin
- 1995