Inequality measures of the generalized gamma distribution with a practicable application tool

Abstract

We introduce the inequality measures of the generalized gamma distribution. The Gini coefficient, Theil, Atkinson and Pietra indexes are considered as the inequality measures. The parameters of the generalized gamma distribution are estimated using the minimum distance estimator based on the Kullback-Leibler divergence for the grouped data. The simulation study is constructed to evaluate the performance of the parameter estimation method under the grouped data. The US income data for three different years are analyzed. Also, the GGIneq web-tool is developed to make the application of the inequality measures easy for the practitioners. The GGIneq, accessible via https://smartstat.shinyapps.io/GGIneq/ , is a cloud-based system that allows users to obtain inequality measures of the generalized gamma distribution with high-quality graphical results.