Abstract
Scientists have analysed different methods for numerical estimation of Gini coefficients. Using Lorenz curves, various numerical integration attempts have been made to identify accurate estimates. Central alternative methods have been the trapezium, Simpson and Lagrange rules. They are all special cases of the Newton-Cotes methods. In this study, we approximate the Lorenz curve by polynomial regression models and integrate optimal regression models for numerical estimation of the Gini coefficient. The attempts are checked on theoretical Lorenz curves and on empirical Lorenz curves with known Gini indices. In all cases the proposed methods seem to be a good alternative to earlier methods presented in the literature.
Highlights
Income distributions are commonly unimodal and skew with a heavy right tail
The attempts are checked on theoretical Lorenz curves and on empirical Lorenz curves with known Gini indices
The Lorenz curves for the Pareto, Chotikapanich and Gupta models are presented in deciles, and we can compare their regression results
Summary
Different skew models, such as the lognormal and the Pareto, have been proposed as suitable descriptions of income distributions, and the corresponding Lorenz curves have been obtained. These are usually applied in specific empirical situations. The Pareto, Chotikapanich and Gupta models contain only one parameter They are so simple that it is impossible to distinguish between the length of the range of the income distribution function and the Gini coefficient. The empirical value of the method is based on analyses of real data in the literature with Gini indices of strong accuracy, and our obtained results are compared with earlier findings
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