Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/45473
Authors: 
Koshevoy, Gleb
Mosler, Karl
Year of Publication: 
1995
Series/Report no.: 
Discussion papers in statistics and econometrics 7/95
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.
Subjects: 
Dilation
Disparity measurement
Gini mean difference
Lift zonoid
Lorenz order
Document Type: 
Working Paper

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