关于衡量收入不平等的加尔各答指数

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摘要翻译：
我们研究了收入不平等的加尔各答(k)指数的数学和经济结构。我们证明了K指数总是存在的，并且是互补Lorenz函数的唯一不动点，其中Lorenz函数本身给出了人口累积部分所拥有的累积收入的分数（当从较穷到较富排列时）。我们证明了K指数推广了Pareto的80/20规则。虽然k指数和Pietra指数都将社会分为两个群体，但我们表明k指数是衡量贫富分化的更密集的指标。我们将归一化K指数与基尼系数和Pietra指数进行了比较，并讨论了它们何时重合。我们证明了对于任何收入分配，基尼系数的值不小于Pietra指数的值，Pietra指数的值不小于归一化K指数的值。基尼系数和Pietra指数只受富人或穷人之间转移的影响，而K指数只受两个群体之间转移的影响。
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英文标题：
《On the Kolkata index as a measure of income inequality》
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作者：
Suchismita Banerjee, Bikas K. Chakrabarti, Manipushpak Mitra, Suresh
  Mutuswami
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最新提交年份：
2019
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分类信息：

一级分类：Economics        经济学
二级分类：Theoretical Economics        理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  We study the mathematical and economic structure of the Kolkata (k) index of income inequality. We show that the k-index always exists and is a unique fixed point of the complementary Lorenz function, where the Lorenz function itself gives the fraction of cumulative income possessed by the cumulative fraction of population (when arranged from poorer to richer). We show that the k-index generalizes Pareto's 80/20 rule. Although the k and Pietra indices both split the society into two groups, we show that k-index is a more intensive measure for the poor-rich split. We compare the normalized k-index with the Gini coefficient and the Pietra index and discuss when they coincide. We establish that for any income distribution the value of Gini coefficient is no less than that of the Pietra index and the value of the Pietra index is no less than that of the normalized k-index. While the Gini coefficient and the Pietra index are affected by transfers exclusively among the rich or among the poor, the k-index is only affected by transfers across the two groups.
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PDF链接：
https://arxiv.org/pdf/1905.03615

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关键词：收入不平等 加尔各答 不平等 Mathematical distribution 穷到 群体 cumulative 给出 转移