The Lorenz Curve and the Gini Coefficient

2003 ◽  
Vol 34 (3) ◽  
pp. 296-296 ◽  
Author(s):  
Robert Rycroft
Keyword(s):  
Gini Coefficient ◽  
Lorenz Curve ◽  
The Gini Coefficient ◽  
The Lorenz Curve

scholarly journals Modified Lorenz Curve and Its Computation

2020 ◽  
Vol 3 (2) ◽  
pp. 99-108
Author(s):  
Subian Saidi ◽  
Ulfah Muharramah ◽  
La Zakaria ◽  
Yomi Mariska ◽  
Triyono Ruby
Keyword(s):  
Income Distribution ◽  
Gini Coefficient ◽  
Lorenz Curve ◽  
Standard Form ◽  
Computer Software ◽  
Computational Techniques ◽  
Computational Results ◽  
Computational Process ◽  
The Gini Coefficient ◽  
The Lorenz Curve

The Lorenz curve is generally used to find out the inequality of income distribution. Mathematically a standard form of the Lorenz curve can be modified with the aim of simplicity of its symmetric analysis and calculation of the Gini coefficient that usually accompanies it. One way to modify the shape of the Lorenz curve without losing its characteristics but is simple in the analysis of geometric shapes is through a transformation (rotation). To be efficient and effective in computing and analyzing a Lorenz curve it is necessary to consider using computer software. In this article, in addition to describing the development of the concept of using transformations (rotations) of the standard Lorenz curve in an easy-to-do form, the symmetric analysis is also described by computational techniques using Mathematica® software. From the results of the application of the development of the concept of the Lorenz curve which is carried out on a data gives a simpler picture of the computational process with relatively similar computational results.

scholarly journals Income inequality measures and the middle class

2021 ◽  
Vol 114 ◽  
pp. 01019
Author(s):  
Oleg I. Pavlov ◽  
Olga Yu. Pavlova
Keyword(s):  
Income Inequality ◽  
Middle Class ◽  
Lower Bounds ◽  
Gini Coefficient ◽  
Lorenz Curve ◽  
Upper And Lower Bounds ◽  
Inequality Measures ◽  
The Gini Coefficient ◽  
Class 1 ◽  
The Lorenz Curve

We study how the presence of the middle class in the sense of Gevorgyan-Malykhin affects the value of income inequality measures including the Gini coefficient J and the Hoover index H. It is proved that in the presence of the middle class (1) $J \leqslant \frac{1}{2}\frac{{L'\left( 0 \right)}}{2}$ (where L is the Lorenz function), (2) $H \leqslant \frac{1}{2}$, (3) the longest vertical distance between the diagonal and the Lorenz curve (which is equal to H) is attained at ${z_0} < \frac{3}{4}$ A tight upper bound for P90/P10 ratio is found assuming L′(0)>0. Tight upper and lower bounds for the differential deviation in terms of the Gini coefficient are found as well.

The Discovery of the Gini Coefficient

2020 ◽  
pp. 115-141
Author(s):  
Michael Schneider
Keyword(s):  
Twentieth Century ◽  
Income Inequality ◽  
Gini Coefficient ◽  
Lorenz Curve ◽  
The Gini Coefficient ◽  
Early Twentieth Century ◽  
Corrado Gini ◽  
The Lorenz Curve

This article traces the development of the methods of representing the degree of income inequality that were developed in the early twentieth century by Max Otto Lorenz and Corrado Gini. It suggests that Gini’s efforts to perfect the Lorenz curve may well have facilitated his discovery of what came to be known as the Gini coefficient and argues that this coefficient is an important example of a multiple (or chain multiple) discovery.

scholarly journals Timetable and Headway Adherence Assessment using the Gini Coefficient and the Lorenz Curve

2021 ◽  
Vol 9 ◽  
pp. 137-151
Author(s):  
Neila Bhouri ◽  
Sneha Lakhotia ◽  
Maurice Aron ◽  
Geetam Tiwari
Keyword(s):  
Gini Coefficient ◽  
Lorenz Curve ◽  
New Delhi ◽  
Time Data ◽  
The Gini Coefficient ◽  
Adherence Assessment ◽  
The Lorenz Curve ◽  
Traffic Disturbance ◽  
Bus Schedule ◽  
The Impact

Adherence to the schedule is of prime importance in public transport. This paper presents a specific application of the Gini coefficient, well known indicator in economics, for the headway adherence assessment. The paper shows that Lorenz curve, which is usually used to define mathematically the Gini coefficient, is a good indicator of the users' waiting time when it is based on the bus schedule. When it is computed on the basis of the ratio of observed headway to the schedule, it is a powerful visual tool that can be used by operators to detect the existence of irregularities on a bus line at a glance. An equation gives, in an idealistic case, the impact of any single traffic disturbance on the Gini coefficient, making this coefficient comprehensive. A detailed analysis is developed, based on the bus proportions according to the headway adherence level. These proportions are obtained from new indices coming from the derivative of the Lorenz curve. The values of these indexes alert the operator of any adherence disturbance. The examination of the Lorenz curve takes more time, but is worthwhile, giving the types of the irregularities The application of these indicators is carried on real-time data from the New Delhi bus network.

scholarly journals MODELS OF DISTRIBUTION OF GDP AT THE GLOBAL LEVEL

2018 ◽  
pp. 177
Author(s):  
Zoran Tomić ◽  
Ognjen Radović
Keyword(s):  
Gini Coefficient ◽  
Lorenz Curve ◽  
Statistical Physics ◽  
Gibbs Distribution ◽  
Global Level ◽  
The Gini Coefficient ◽  
Pareto Model ◽  
The Lorenz Curve

Problem of distribution gathers the attention of researchers for years. In their research they analyze the uniformity of distribution using Pareto model of distribution, the Lorenz curve and the Gini coefficient. Also some authors are testing the applicability of models from statistical physics to the problem of distribution to better describe it. In addition to the analysis of distribution at the level of states and certain groups such as the Forbes list, the problem is spreading to the global level, where we analyze the distribution of GDP as a measure of the wealth of individual countries.In this paper we analyzed the distribution of GDP of countries applying the Pareto model, Lorenz curve, Gini coefficient and Boltzmann Gibbs distribution from statistical physics. The analysis was done for 2015, while the Gini coefficient analysis was done during the period from 1990 to 2015.

A Study of the Estimation of the Gini Coefficient of Income Using Lorenz Curve

2016 ◽  
Vol 15 (4) ◽  
pp. 1-10 ◽  
Author(s):  
Kwasi Darkwah ◽  
Ezekiel Nortey ◽  
Felix Mettle ◽  
Isaac Baidoo
Keyword(s):  
Gini Coefficient ◽  
Lorenz Curve ◽  
The Gini Coefficient

INCOME DISTRIBUTION OF RED CHILLI FARMER, AT MEREMBU VILLAGE, LABUAPI DISTRICT, WEST LOMBOK REGENCY 2021

2021 ◽  
Vol 1 (2) ◽  
pp. 27-33
Author(s):  
Ida Bagus Eka Artika
Keyword(s):  
Income Distribution ◽  
World Bank ◽  
Gini Coefficient ◽  
Lorenz Curve ◽  
Research Area ◽  
Distribution Analysis ◽  
Agricultural Commodity ◽  
The World Bank ◽  
The World ◽  
The Lorenz Curve

Red chili is an agricultural commodity planted by farmers on the sidelines of rice planting as the main agricultural commodity, especially in Merembu Village, Labuapi District, West Lombok Regency. This study aims to determine the level of income distribution of chili farmers in Merembu Village, Labuapi District, West Lombok Regency. The sample respondent as many as 35 red chili farmers in the research area. The analysis technique uses income distribution analysis with three approaches, namely Gini Coefficient approach, Lorenz Curve and World Bank Criteria Approach. The results of the Gini Ratio calculation for the 35 respondents studied, obtained a Gini Index or Gini Coefficient of 0.143, this shows the income inequality of red chili farmers in Merembu Village, Labuapi District in the mild or low category. This statement is reinforced by the Lorenz Curve approach and the World Bank Criteria Approach, namely the results of calculations based on the World Bank approach obtained that 40% of the population with low incomes receive an income of 29.6% or greater than 17% (Low Category) of the total existing income. This indicates that the category of the level of income distribution of chili farmers in Merembu Village, Labuapi District is relatively low

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