scholarly journals A comparative study of the Gini coefficient estimators based on the linearization and U-statistics Methods

2017 ◽  
Vol 40 (2) ◽  
pp. 205-221 ◽  
Author(s):  
Shahryar Mirzaei ◽  
Gholam Reza Mohtashami Borzadaran ◽  
Mohammad Amini
Keyword(s):  
Comparative Study ◽  
Simulation Study ◽  
Gini Coefficient ◽  
Gini Index ◽  
Real Data ◽  
Linearization Method ◽  
U Statistics ◽  
The Gini Coefficient

In this paper, we consider two well-known methods for analysis of the Gini index, which are U-statistics and linearization for some incomedistributions. In addition, we evaluate two different methods for some properties of their proposed estimators. Also, we compare two methods with resampling techniques in approximating some properties of the Gini index. A simulation study shows that the linearization method performs 'well' compared to the Gini estimator based on U-statistics. A brief study on real data supports our findings.

scholarly journals Inequality Measures: The Kolkata Index in Comparison With Other Measures

2020 ◽  
Vol 8 ◽  
Author(s):  
Suchismita Banerjee ◽  
Bikas K. Chakrabarti ◽  
Manipushpak Mitra ◽  
Suresh Mutuswami
Keyword(s):  
Gini Coefficient ◽  
Gini Index ◽  
Empirical Studies ◽  
Nonlinear Function ◽  
Hirsch Index ◽  
Inequality Measures ◽  
Income Distributions ◽  
The Gini Coefficient ◽  
The Rich ◽  
Total Wealth

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.

Measuring and Explaining Economic Inequality

2013 ◽  
pp. 87-101
Author(s):  
C. Chameni Nembua
Keyword(s):  
Case Studies ◽  
Gini Coefficient ◽  
Gini Index ◽  
Economic Inequality ◽  
Transfer Principle ◽  
New Class ◽  
The Gini Coefficient ◽  
The One ◽  
Theoretical Results ◽  
Subgroup Decomposition

This chapter proposes a new class of inequality indices based on the Gini coefficient (or index). The properties of the indices are studied and are found to be regular, relative, and to satisfy the Pigou-Dalton transfer principle. A subgroup decomposition is performed, and the method is found to be similar to the one used by Dagum when decomposing the Gini index. The theoretical results are illustrated by case studies, using Cameroonian data.

scholarly journals Confidence Intervals of Gini Coefficient Under Unequal Probability Sampling

2020 ◽  
Vol 36 (2) ◽  
pp. 237-249
Author(s):  
Yves G. Berger ◽  
İklim Gedik Balay
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Empirical Likelihood ◽  
Simulation Study ◽  
Gini Coefficient ◽  
Probability Sampling ◽  
Unequal Probability Sampling ◽  
Unequal Probability ◽  
The Gini Coefficient

AbstractWe propose an estimator for the Gini coefficient, based on a ratio of means. We show how bootstrap and empirical likelihood can be combined to construct confidence intervals. Our simulation study shows the estimator proposed is usually less biased than customary estimators. The observed coverages of the empirical likelihood confidence interval proposed are also closer to the nominal value.

scholarly journals A comparative study of the Gini coefficient estimators based on the regression approach

2017 ◽  
Vol 24 (4) ◽  
pp. 339-351
Author(s):  
Shahryar Mirzaei ◽  
Gholam Reza Mohtashami Borzadaran ◽  
Mohammad Amini ◽  
Hadi Jabbari
Keyword(s):  
Comparative Study ◽  
Gini Coefficient ◽  
The Gini Coefficient ◽  
Regression Approach

scholarly journals Transforming variables to central normality

2021 ◽  
Author(s):  
Jakob Raymaekers ◽  
Peter J. Rousseeuw
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Real Data ◽  
Data Sets ◽  
Transformation Parameter ◽  
Likelihood Estimator ◽  
Extensive Simulation ◽  
Highly Sensitive

AbstractMany real data sets contain numerical features (variables) whose distribution is far from normal (Gaussian). Instead, their distribution is often skewed. In order to handle such data it is customary to preprocess the variables to make them more normal. The Box–Cox and Yeo–Johnson transformations are well-known tools for this. However, the standard maximum likelihood estimator of their transformation parameter is highly sensitive to outliers, and will often try to move outliers inward at the expense of the normality of the central part of the data. We propose a modification of these transformations as well as an estimator of the transformation parameter that is robust to outliers, so the transformed data can be approximately normal in the center and a few outliers may deviate from it. It compares favorably to existing techniques in an extensive simulation study and on real data.

scholarly journals Why We Should Use the Gini Coefficient to Assess Punctuated Equilibrium Theory

2021 ◽  
pp. 1-6
Author(s):  
Constantin Kaplaner ◽  
Yves Steinebach
Keyword(s):  
Policy Change ◽  
Gini Coefficient ◽  
Policy Making ◽  
Punctuated Equilibrium ◽  
Equilibrium Theory ◽  
Punctuated Equilibrium Theory ◽  
The Gini Coefficient ◽  
Precise Measure

Abstract Punctuated Equilibrium Theory posits that policy-making is generally characterized by long periods of stability that are interrupted by short periods of fundamental policy change. The literature converged on the measure of kurtosis and L-kurtosis to assess these change patterns. In this letter, we critically discuss these measures and propose the Gini coefficient as a (1) comparable, but (2) more intuitive, and (3) more precise measure of “punctuated” change patterns.

The Gini coefficient: Majority voting and social welfare

2014 ◽  
Vol 152 ◽  
pp. 214-223 ◽  
Author(s):  
Juan Gabriel Rodríguez ◽  
Rafael Salas
Keyword(s):  
Social Welfare ◽  
Gini Coefficient ◽  
Majority Voting ◽  
The Gini Coefficient
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