Characterizations of Lorenz curves and income distributions

Aaberge, Rolf

doi:10.1007/s003550000046

Cited by 111 publications

(144 citation statements)

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“…By observing that the Lorenz curve can be considered analogous to a cumulative distribution function Aaberge (2000) demonstrated that the moments of the Lorenz curve generate the following family of inequality measures…”

Section: Gini's Nuclear Family Of Inequality Measuresmentioning

confidence: 99%

“…By exploiting the fact that the Lorenz curve can be considered analogous to a cumulative distribution function, Aaberge (2000) draws on standard statistical practice to justify the use of the first few moments of the Lorenz curve (LC-moments) as basis for summarizing the information content of the Lorenz curve. However, considered as a group these measures suffer from a drawback since none of them in general are particularly sensitive to changes that concern the lower part of the income distribution.…”

Section: Introductionmentioning

confidence: 99%

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Gini’s nuclear family

Aaberge

2007

J Econ Inequal

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The purpose of this paper is to justify the use of the Gini coefficient and two close relatives for summarizing the basic information of inequality in distributions of income. To this end we employ a specific transformation of the Lorenz curve, the scaled conditional mean curve, rather than the Lorenz curve as the basic formal representation of inequality in distributions of income. The scaled conditional mean curve is shown to possess several attractive properties as an alternative interpretation of the information content of the Lorenz curve and furthermore proves to yield essential information on polarization in the population. The paper also provides asymptotic distribution results for the empirical scaled conditional mean curve and the related family of empirical measures of inequality. Keywords:The scaled conditional mean curve, measures of inequality, the Gini coefficient, the Bonferroni coefficient, measures of social welfare, principles of transfer sensitivity, estimation, asymptotic distributions. JEL classification: D3, D63.Acknowledgement: This paper was written when the author was visiting ICER in Torino. ICER and the Norwegian Research Council are gratefully acknowledged for providing financial support. I wish to thank Jacques Silber, Terje Skjerpen and two referees for helpful comments.

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Section: Gini's Nuclear Family Of Inequality Measuresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Gini’s nuclear family

Aaberge

2007

J Econ Inequal

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“…1 For example the Gini 9,26-28 of that distribution tells about the distortion in the income distribution, therefore, suggests to research on whether the opportunities are based on abilities and e®orts rather than on \crony economics" and other biases (e.g., corruption). Gini is a number, 0 Gini 1, where the Gini formula is [26][27][28][29][30][31][32][33][34][35][36] Gini ¼ 1 hci…”

Section: Introductionmentioning

confidence: 99%

The IncomeGini of Fairness

Flomenbom¹

2017

Rep. Adv. Phys. Sci.

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We are in favor of wealth accumulation in a free and democratic nation. Yet, the question is whether the mechanism of wealth accumulation is the same to all the people or are there di®erent mechanisms to di®erent socioeconomic-groups, therefore unfair biases in the nation. Here, we would like to develop ways to quantify and¯ght there unfair distortions. Utilizing methods from socioecono-physics, we¯nd that in a democratic and a free nation, a fair society is such that the income distribution's Gini is in the range, 25% and 33%, 34%. (Gini is the departure of the distribution from the \all are equal" distribution). The value, Gini % 40%, is indeed the transition from the intermediate stage nation to the corrupt nation, where Gini 40% requires that the income distribution is smooth in the top percentiles (rather than a jump like formed). Therefore, the e®ect of the 0.1% excessive wealth is pivotal to the problem; such nations have Gini values beyond 40%. The wealth distribution's properties further strengthen these¯ndings.We develop a dynamical model that is emphasizing the di®erence in the environment of the two camps: the top and the rest, yet¯nd that interactions create a smoother income density.We therefore think that the income distribution's Gini % 40% is the alarm stage, yet the Gini should better follow the middle range of the fair society stage (25% through 33%) rather than the upper bound in that stage, where ways to realize that are elaborated on.

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“…The methodological and applicative works on that subject are so numerous that it is very difficult to choose even a small selection. Aaberge (2000); Groves-Kirkby et al (2009) and Jacobson et al (2005) can be mentioned in order to highlight the importance of Lorenz curve regarding applications in different scientific fields. Nevertheless, several alternative tools for evaluating the inequality have been proposed in literature e.g, the inequality curve by Zenga (2007).…”

Section: Introductionmentioning

confidence: 99%

Reliability and Inequality Measures for the Weimal Distribution

Ieren¹,

Yahaya²

2017

Nig J Bas App Sci

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Reliability analysis basically deals with the probability of survival or failure (death). This article aimed at discussing both reliability and inequality measures from the Weimal distribution. The work has derived and discussed theoretically, expressions for the survival and hazard function of the Weimal distribution. The ordinary and incomplete moments of the distribution were also obtained. Lastly, some inequality measures for the distribution were derived using the moments of the distribution.

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Characterizations of Lorenz curves and income distributions

Cited by 111 publications

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Gini’s nuclear family

Gini’s nuclear family

The IncomeGini of Fairness

Reliability and Inequality Measures for the Weimal Distribution

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