广义洛伦茨指数的构造及应用

The Constructions and Applications of Generalized Lorenz Index

研究目标:提出并构造广义洛伦茨指数,并阐释它的优良性质和应用价值。研究方法:对一类定义在洛伦茨曲线族上的不平等指数进行理论分析,探究其联系和区别,进而构造统一框架,并与广义熵指数类进行比较。研究发现:不平等实证度量的本质是基于实际收入分布对收入绝对平等状态的偏离程度,进行信息的加工和压缩。现有不平等度量指标主要分为广义熵指数类和洛伦茨曲线指数类,前者基于信息论中熵的概念,后者基于泛函分析中伪距离的概念,本文在此基础上构造了广义洛伦茨指数,基尼系数、Bonferroni指数、De Vergottini指数等都是它的特例。研究创新:构造统一框架,将一大类不平等度量指数一般化。研究价值:揭示了各种不平等度量指标间的关系,对“不平等度量的稳健性”进行了考察。

Research Objectives:This paper is to propose and construct Generalized Lorenz Index,and reveal its property and application.Research Methods:To investigate a class of inequality indices defined on the Lorenz curve family based on the relation and difference,the unified framework is constructed and compared with the generalized entropy index class.Research Findings:The essence of empirical measurement of inequality is to measure the degree of deviation between the Lorenz curve(real income distribution)and the absolute equal line(absolute equality of income).The existing inequality indices are mainly divided into Generalized Entropy Index and Generalized Lorenz Index.The former is based on the concept of entropy in information theory,and the latter is based on the concept of pseudometric in functional analysis.The Gini coefficient is a special pseudometric,which measures the degree of deviation between the Lorenz curve and the absolute equal line.The Bonferroni index and the De Vergottini index can also be defined as other different pseudometric.The Gini coefficient,Bonferroni index,De Vergottini index and a new inequality index GL(1,1,1)are all special cases of Generalized Lorenz Index.Research Innovations:We give the Lorenz curves family a topological structure and try to construct a unified framework to generalize a class of inequality metrics defined in the Lorentz curves family.Research Value:We reveal the essential connections and differences between various commonly used inequality indexes,and investigate the robustness of measure of inequality indexes.