On the Kolkata index as a measure of income inequality

Banerjee, Suchismita; Chakrabarti, Bikas K.; Mitra, Manipushpak; Mutuswami, Suresh

doi:10.1016/j.physa.2019.123178

Cited by 17 publications

(32 citation statements)

References 10 publications

(13 reference statements)

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“…Ref. 3, is that proportion k of the population such that the proportion of income that we can associate with k is (1 − k). Since no single summary statistic can reflect all aspects of inequality exhibited by the Lorenz curve, the importance of using alternative measures of inequality is universally acknowledged (see Ref.…”

Section: And Later Analyzed In Ref 2 and Inmentioning

confidence: 99%

“…This example is taken from Ref. 3. Let us consider an arc of a unit circle ODB as a Lorenz curve where OB is one of the diagonal (egalitarian line) of the unit square ABCO (as shown in Figure 3) where CD represents the unit radius of the circle, CA is the other diagonal of the unit square ABCO 2 √ .…”

Section: Comparison Of Magnitudesmentioning

confidence: 99%

“…Since the way inequality is measured also determines how the above questions (among others) are answered, a rigorous discussion of the measurement of inequality is necessary (see, e.g., Refs. [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

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Inequality Measures: The Kolkata Index in Comparison With Other Measures

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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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Section: And Later Analyzed In Ref 2 and Inmentioning

confidence: 99%

Section: Comparison Of Magnitudesmentioning

confidence: 99%

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Inequality Measures: The Kolkata Index in Comparison With Other Measures

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“…Согласно эмпирическим исследованиям (Ghosh, Chattopadhyay and Chakrabarti, 2014), (Inoue et al, 2015), (Chatterjee, Ghosh and Chakrabarti, 2017), (Banerjee et al, 2020), 100 000 1 000 000 10 000 000 100 000 000…”

Section: модель кривой паретоunclassified

Распределение Размеров Штатов, Округов И Городов США: Новая Информация О Форме Неравенства

Grachev¹

2020

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В статье предлагается новый подход к исследованию закономерностей распределения размеров в системах расселения, основанный на анализе формы кривой Парето (PC). Для изучения формы PC использованы коэффициент Джини, асимметрии и, по аналогии с физикой фазовых переходов, показатель степени PC в окрестности нуля. Выполнен эмпирический анализ PC различных уровней агрегации системы расселения США. Форму распределения размеров штатов исследовали по десятилетиям с 1790 по 2010 год. Пространственный анализ формы PC округов и городов выполнен для 2010 года. Результаты проведенного эмпирического исследования показали, что PC штатов на протяжении 220 лет имела левостороннюю асимметрию. PC округов и городов имела как правостороннюю, так и левостороннюю асимметрию. Полученные результаты объясняют, в каких случаях распределение Парето, имеющее PC с правосторонней асимметрией, и логнормальное распределение с симметричной PC объективно могут не соответствовать реальным системам расселения. В качестве альтернативы степенному и логнормальному распределению рассмотрена аналитически простая двухпараметрическая модель с широким диапазоном асимметрии PC, объединяющая в себе свойства комбинации степенного и логнормального распределений. Верификация модели показала, что она адекватно описывает размеры поселений однородных систем расселения.

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“…According to an empirical study (Ghosh, Chattopadhyay and Chakrabarti, 2014;Inoue et al, 2015;Chatterjee, Ghosh and Chakrabarti, 2017;Banerjee et al, 2020), with 6 0.…”

Section: The Pareto Curve Modelmentioning

confidence: 99%

Size Distribution of States, Counties, and Cities in the USA: New Inequality Form Information

Grachev

2020

Preprint

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In this article, we propose a new approach for studying the patterns of size distribution in settlement systems, based on the analysis of the shape of the Pareto curve (PC). To study the shape of the PC, we used the Gini coefficient, the asymmetry coefficient, and, by analogy with the physics of phase transitions, critical exponent — the index of the PC degree in the neighborhood of zero. An empirical analysis of the PC of various levels of aggregation in the US settlement system has been performed. The form of size distribution of states was studied by decades from 1790 to 2010. The spatial analysis of the PC shape for counties and cities was performed for 2010. The results of an empirical study showed that the PC of the states had left-hand asymmetry over 220 years. The PC of districts and cities had both right-hand and left-hand asymmetries. The obtained results explain in which cases the Pareto distribution having a PC with right-hand asymmetry, and the lognormal distribution with a symmetric PC may not correspond objectively to real settlement systems. As an alternative to power-series distribution and lognormal distribution, we considered an analytically simple two-parameter model with a wide range of PC asymmetry that combines the properties of power-series distribution and lognormal distribution. Verification of the model showed that it adequately described the size of settlements in homogeneous settlement systems.

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On the Kolkata index as a measure of income inequality

Cited by 17 publications

References 10 publications

Inequality Measures: The Kolkata Index in Comparison With Other Measures

Inequality Measures: The Kolkata Index in Comparison With Other Measures

Распределение Размеров Штатов, Округов И Городов США: Новая Информация О Форме Неравенства

Size Distribution of States, Counties, and Cities in the USA: New Inequality Form Information

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