不平等指标：加尔各答指数与其他指标的比较
Inequality Measures: The Kolkata index in comparison with other measures
摘要：
我们提供了一个社会不平等的加尔各答指数的调查，特别侧重于收入不平等。根据观察，不平等的功能（如洛伦兹函数），给出的措施，收入或财富对人口，一般是非线性的，我们表明，不动点（如加尔各答指数k）这样一个非线性函数（或相关的，如补充洛伦兹函数）提供更好的措施不平等的平均数量（如基尼指数）。事实上，加尔各答指数可以被看作是一个广义的赫希指数的一个归一化的不平等功能，并给出了分数k的总财富所拥有的富裕（1-k）部分的人口。我们分析了连续和离散收入分配的不平等指数的结构。我们还比较了加尔各答指数的一些其他措施，如基尼系数和皮特拉指数。最后，我们提供了一些实证研究，说明加尔各答指数和基尼系数之间的差异。
英文摘要：
We provide a survey of the Kolkata index of social inequality, focusing in particular on income inequality. Based on the observation that inequality functions (such as the Lorenz function), giving the measures of income or wealth against that of the population, to be generally nonlinear, we show that the fixed point (like Kolkata index k) of such a nonlinear function (or related, like the complementary Lorenz function) offer better measure of inequality than the average quantities (like Gini index). Indeed the Kolkata index can be viewed as a generalized Hirsch index for a normalized inequality function and gives the fraction k of the total wealth possessed by the rich (1-k) fraction of the population. We analyze the structures of the inequality indices for both continuous and discrete income distributions. We also compare the Kolkata index to some other measures like the Gini coefficient and the Pietra index. Lastly, we provide some empirical studies which illustrate the differences between the Kolkata index and the Gini coefficient.
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