Multivariate Gini indices

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Discussion Papers in Statistics and Econometrics ; No. 7/95

Classification and Topics

• Classification: Wirtschaft
• Subject: Dilation ; Disparity measurement ; Gini mean difference ; Lift zonoid ; Lorenz order

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Koshevoy, Gleb ; Mosler, Karl
• Event: Veröffentlichung
• (who): University of Cologne, Seminar of Economic and Social Statistics
• (where): Cologne
• (when): 1995

Further information

• Handle: http://hdl.handle.net/10419/45473
• Last update: 10.03.2025, 11:43 AM CET