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Uni Köln > WiSo-Fakultät > Seminar für Wirtschafts- und Sozialstatistik > Institut > LS Mosler > Prof. Mosler > Publikationen
Publikationen von Univ.-Prof. Dr. Karl Mosler |
Abstract: Multivariate Gini indices (Gleb Koshevoy and Karl Mosler) |
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Two extensions of the univariate Gini index are considered: 
(Arnold, 1987) based on expected distance between two independent vectors
from the same distribution with finite mean 
and 
(Wilks, 1960) related to the expected volume of the simplex formed from
d+1 independent such vectors. A new characterization of
as proportional to a univariate Gini index for a particular linear combination
of attributes relates it with the Lorenz zonoid. The Lorenz zonoid
was suggested by Koshevoy and Mosler (1996) as a multivariate generalization
of the Lorenz curve.
is, up to scaling, the volume of the Lorenz zonoid plus a unit cube of
full dimension. When d=1, both
and
equal twice the area between the usual Lorenz curve and the line of zero
disparity. When d>1, they are different, but inherit properties
of the univariate Gini index and are related via the Lorenz zonoid:
is proportional to the average of the areas of some two-dimensioned projections
of the lift zonoid, while
is the average of the volumes of projections of the Lorenz zonoid over
all coordinate subspaces. |
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Keywords and -phrases: dilation, disparity measurement, Gini mean difference, lift zonoid, Lorenz order. |
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