In this paper, we characterize some new links between stochastic dominance and the measurement of inequality and poverty. We show that: for second‐degree normalized stochastic dominance (NSD), the weighted area between the NSD curve of a distribution and that of the equalized distribution is a decomposable inequality measure; for first‐degree and second‐degree censored stochastic dominance (CSD), the weighted area between the CSD curve of a distribution and that of the zero‐poverty distribution is a decomposable poverty measure. These characterizations provide graphical representations for decomposable inequality and poverty measures in the same manner as Lorenz curve does for the Gini index. The extensions of the links to higher degrees of stochastic dominance are also investigated.

中文翻译：

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随机优势和不平等与贫困的可分解衡量

在本文中，我们描述了随机支配地位与不平等和贫困程度之间的一些新联系。我们表明：对于二次归一化随机优势（NSD），分布的NSD曲线和均衡分布的NSD曲线之间的加权面积是可分解的不等式测度；对于一阶和二阶删失随机优势（CSD），分布的CSD曲线和零贫困分布的CSD曲线之间的加权区域是可分解的贫困度量。这些特征以可分解的不平等和贫困测度的图形表示方式，与洛伦兹曲线对基尼系数的表示方式相同。链接的扩展到更高程度的随机支配地位也得到了研究。