scholarly journals Estimating Gini Coefficient from Grouped Data Based on Shape-Preserving Cubic Hermite Interpolation of Lorenz Curve

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2551
Author(s):  
Songpu Shang ◽  
Songhao Shang
Keyword(s):  
Gini Coefficient ◽  
Lorenz Curve ◽  
Strain Energy ◽  
Hermite Interpolation ◽  
Interpolation Method ◽  
Grouped Data ◽  
Shape Preserving ◽  
Unequally Spaced ◽  
Interpolation Curve ◽  
The Lorenz Curve

The Lorenz curve and Gini coefficient are widely used to describe inequalities in many fields, but accurate estimation of the Gini coefficient is still difficult for grouped data with fewer groups. We proposed a shape-preserving cubic Hermite interpolation method to approximate the Lorenz curve by maximizing or minimizing the strain energy or curvature variation energy of the interpolation curve, and a method to estimate the Gini coefficient directly from the coefficients of the interpolation curve. This interpolation method can preserve the essential requirements of the Lorenz curve, i.e., non-negativity, monotonicity, and convexity, and can estimate the derivatives at intermediate points and endpoints at the same time. These methods were tested with 16 grouped quintiles or unequally spaced datasets, and the results were compared with the true Gini coefficients calculated with all census data and results estimated with other methods. Results indicate that the maximum strain energy interpolation method generally performs the best among different methods, which is applicable to both equally and unequally spaced grouped datasets with higher precision, especially for grouped data with fewer groups.

The Interpolation of the Lorenz Curve and Gini Index from Grouped Data

Econometrica ◽  
1976 ◽  
Vol 44 (3) ◽  
pp. 479 ◽  
Author(s):  
Joseph L. Gastwirth ◽  
Marcia Glauberman
Keyword(s):  
Lorenz Curve ◽  
Gini Index ◽  
Grouped Data ◽  
The Lorenz Curve

Lorenz Curve Interpolation and the Gini Coefficient

2010 ◽  
Author(s):  
Nicholas Charles Rohde
Keyword(s):  
Gini Coefficient ◽  
Lorenz Curve ◽  
Polynomial Spline ◽  
The Philippines ◽  
The Body ◽  
Grouped Data ◽  
Parametric Methods ◽  
Lorenz Curves ◽  
Curve Interpolation ◽  
Income Decile

This article presents a simple non-polynomial spline that may be used to construct Lorenz curves from grouped data. The spline is naturally convex and works by determining a series of piecewise segments that may be joined to give a smooth and continuous Lorenz curve. The method is illustrated with an empirical example using income decile data from the Philippines from 1991-2003 where the proposed technique is used alongside other parametric and non-parametric methods. We also use the spline to approximate some known Lorenz curves and assess the technique by comparing the estimated Gini coefficient to the known Gini. Our findings suggest that the method is an attractive addition to the body of techniques used for developing Lorenz curves from grouped data.

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

scholarly journals Assessment of the income situation of households in the Czech Republic

2011 ◽  
Vol 57 (No. 7) ◽  
pp. 322-330
Author(s):  
J. Turčínková ◽  
J. Stávková
Keyword(s):  
Czech Republic ◽  
Gini Coefficient ◽  
Household Income ◽  
Lorenz Curve ◽  
Explanatory Power ◽  
Primary Source ◽  
The Czech Republic ◽  
Poverty Threshold ◽  
Average Household Income ◽  
The Lorenz Curve

The paper deals with the assessment of income situation of households in the Czech Republic. The primary source for the analysis were the data of the survey EU-SILC European Union – Statistics on Income and Living Conditions. The basic variable for the analysis is the level of the household income in 2005–2008. In addition to the decile classification, characteristics such as the average income per one household member, poverty threshold, poverty depth coefficient, Lorenz curve and Gini coefficient. were calculated in order to evaluate the income situation. The results show an increase of the average household income. The Lorenz curve followed by the Gini coefficient demonstrate the uniformity of distribution of income values. The results show a decreasing income differentiation. The poverty threshold was defined on the level of 60% of the median value and with this given threshold, the households were assessed, whether they belong to the ones at the risk of poverty. The results reveal a decreasing number of households at the risk of poverty. The poverty depth coefficient has a stronger explanatory power and shows how far below the poverty threshold the households are, or what is an income deficit of these households. Each category of households at the risk of poverty varies with the depth of poverty. The analysis also provides the results of how the households' income situation or poverty is perceived by the households themselves.

scholarly journals The Advantages of Using Group Means in Estimating the Lorenz Curve and Gini Index From Grouped Data

2016 ◽  
Vol 70 (1) ◽  
pp. 25-32 ◽  
Author(s):  
Merritt Lyon ◽  
Li C. Cheung ◽  
Joseph L. Gastwirth
Keyword(s):  
Lorenz Curve ◽  
Gini Index ◽  
Grouped Data ◽  
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.

Poverty Incidence and Income Inequality in the Tribal and Non-tribal Area of Central Gujarat

2021 ◽  
Keyword(s):  
Income Inequality ◽  
Gini Coefficient ◽  
Lorenz Curve ◽  
Farm Households ◽  
Graphical Form ◽  
Poor People ◽  
Tribal Area ◽  
Poor Households ◽  
The Lorenz Curve ◽  
Tribal Areas

The present investigation undertook to study the poverty incidence and income distribution among poor and non-poor in the tribal and non-tribal areas applying headcount index and the Gini index, and Lorenz curve. The headcount index shows the proportion of poor households. It shows that poverty was higher in the tribal area than in non-tribal regions. Incidence of poverty was higher in marginal farm households, followed by landless agricultural labour and small farm households. Income inequalities are depicted by the Gini coefficient and presented in graphical form by the Lorenz curve. It showed that total income was distributed more equally among poor and non-poor people in the tribal area than in non-tribal regions. It also observed that in the tribal district, poor and non-poor households had the same proportion of inequality. It was suggested to focus on creating employment opportunities through programmes like MGNREGA to eliminate poverty in particular tribal areas. Keywords: Gini coefficient, headcount index, income inequality, Lorenz curve, poverty incidence. JEL Codes: D63, I32, I38, O15

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