Income modeling with the Weibull mixtures

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.

Keywords:

• Weibull mixture models
• maximum likelihood estimation
• income data
• information criteria

JEL classification:

• C13
• C51
• C52

Acknowledgments

The authors would like to thank the Editor and the referees for their useful comments which greatly improved the paper.

Additional information

Funding

The second author acknowledges support from University of Malaya, Faculty Research Grant (GPF028B-2018).