Abstract

In this paper, we introduce six Weibull based mixture distributions to model income data. Several statistical properties of these models are derived and their closed forms are presented. The mixture model parameters are estimated using the maximum likelihood method and their performances are assessed with respect to average income per tax unit data for ten countries using information based criteria approaches as well as graphical observations. In addition, we provide application of these models to two popular inequality measures, the Gini and Bonferroni indexes as well as the common generalized entropy index. Analytic expressions of the poverty measures are given for head-count ratio and poverty-gap ratio. All the mixture models show good fit to the data with close proximity to empirical Gini and Bonferroni indexes in almost all ten countries where the income data sets are studied.

摘要

在本文中，我们介绍了六个基于 Weibull 的混合分布来模拟收入数据。导出了这些模型的几个统计特性，并给出了它们的封闭形式。使用最大似然法估计混合模型参数，并使用基于信息的标准方法以及图形观察，针对十个国家的每税单位平均收入数据评估其性能。此外，我们将这些模型应用于两种流行的不平等度量，即 Gini 和 Bonferroni 指数以及常见的广义熵指数。给出了贫困人口比和贫困差距比的贫困指标分析表达式。