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.

Sprache
Englisch

Erschienen in
Series: Discussion Papers in Statistics and Econometrics ; No. 7/95

Klassifikation
Wirtschaft
Thema
Dilation
Disparity measurement
Gini mean difference
Lift zonoid
Lorenz order

Ereignis
Geistige Schöpfung
(wer)
Koshevoy, Gleb
Mosler, Karl
Ereignis
Veröffentlichung
(wer)
University of Cologne, Seminar of Economic and Social Statistics
(wo)
Cologne
(wann)
1995

Handle
Letzte Aktualisierung
10.03.2025, 11:43 MEZ

Datenpartner

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Objekttyp

  • Arbeitspapier

Beteiligte

  • Koshevoy, Gleb
  • Mosler, Karl
  • University of Cologne, Seminar of Economic and Social Statistics

Entstanden

  • 1995

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