Regression Analyses of Income Inequality Indices

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.