scholarly journals Axiomatic Characterization of the Gini Coefficient and Lorenz Curve Orderings

2001 ◽  
Vol 101 (1) ◽  
pp. 115-132 ◽  
Author(s):  
Rolf Aaberge
Keyword(s):  
Gini Coefficient ◽  
Lorenz Curve ◽  
Axiomatic Characterization ◽  
The Gini Coefficient

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

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 Group averaging and the Gini deviation

2021 ◽  
Vol 29 (3) ◽  
pp. 595-605
Author(s):  
Oleg I. Pavlov ◽  
Olga Yu. Pavlova
Keyword(s):  
Gini Coefficient ◽  
Upper Bound ◽  
Lorenz Curve ◽  
Piecewise Linear ◽  
Geometric Parameters ◽  
Natural Question ◽  
Lorenz Curves ◽  
The Gini Coefficient ◽  
The Difference ◽  
Group Averaging

It is known that partitioning a society into groups with subsequent averaging in each group decreases the Gini coefficient. The resulting Lorenz function is piecewise linear. This study deals with a natural question: by how much the Gini coefficient could decrease when passing to a piecewise linear Lorenz function? Obtained results are quite illustrative (since they are expressed in terms of the geometric parameters of the polygon Lorenz curve, such as the lengths of its segments and the angles between successive segments) upper bound estimates for the maximum possible change in the Gini coefficient with a restriction on the group shares, or on the difference between the averaged values of the attribute for consecutive groups. It is shown that there exist Lorenz curves with the Gini coefficient arbitrarily close to one, and at the same time with the Gini coefficient of the averaged society arbitrarily close to zero.

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.

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