Two competitor inequality indices in Burr XII distribution
Among many income distributions, the Burr XII distribution has gathered special attention on fitting income data in economic and applied statistics. Recently, several attempts have been made in order to decide which measure of inequality is more suitable for showing inequality in a given subject. So, in this paper, we consider two well-known income inequality indices which are Gini and Zenga for the Burr XII model. In this distribution, the general forms of the Zenga and Gini measures are presented. In addition, we investigate the role of the shape and scale parameters in Gini and Zenga indices and related curves. Also, the stochastic orders based on curves have been discussed. In order to show the good behavior of the Burr XII model to described income distribution, an application using a real data (US household incomes) is presented. Then, some simulation studies based on Burr XII distribution (fitted model) are performed in order to compare and evaluate the performance of the Gini and Zenga measures from a point of view of their statistical properties. Furthermore, the theoretical results have been then tested successfully in real income data sets.
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