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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: The Lorenz Zonoid of a Multivariate Distribution (Gleb Koshevoy and Karl Mosler) |
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The paper extends the usual Lorenz curve and Lorenz order of univariate
distributions to the multivariate case. For a given probability distribution
in nonnegative d-space, 
, we define and investigate the Lorenz zonoid and the Lorenz surface, which
are sets in (d+1)-space. The surface equals the usual Lorenz curve
when d=1. Included is the definition of the Lorenz surface of a
finite number of vectors which may be interpreted as the endowments of
economic units in d commodities. As a notion of increasing multivariate
disparity, we introduce the set inclusion of Lorenz zonoids and show that
it is equivalent to directional majorization.
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Keywords: Multivariate disparity, Lorenz curve, Lorenz surface, Gini
measure, economic inequality measurement. |
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