The Lorenz zonoid of a multivariate distribution

被引：58

作者：

Koshevoy, G ^{[1
]}

Mosler, K ^{[1
]}

机构：

[1] UNIV COLOGNE,D-50923 COLOGNE,GERMANY

来源：

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION | 1996年 / 91卷 / 434期

关键词：

economic inequality measurement; Gini measure; Lorenz curve; Lorenz surface; multivariate disparity;

D O I：

10.2307/2291682

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The article extends the usual Lorenz curve and Lorenz order of univariate distributions to the multivariate case. For a given probability distribution in nonnegative d space, a greater than or equal to 1, 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 that 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.

引用

页码：873 / 882

页数：10

共 25 条

[1]

[Anonymous], 1979, Multivariate analysis

[2]

Arnold BC, 1987, Lecture Notes in Statistics

[3] THE COMPARISON OF MULTI-DIMENSIONED DISTRIBUTIONS OF ECONOMIC-STATUS [J].