A new generalized Weibull distribution in income economic inequality curves

ABSTRACT

Researchers have been developing various extensions and modified forms of the Weibull distribution to enhance its capability for modeling and fitting different data sets. In this note, we investigate the potential usefulness of the new modification to the standard Weibull distribution called odd Weibull distribution in income economic inequality studies. Some mathematical and statistical properties of this model are proposed. We obtain explicit expressions for the first incomplete moment, quantile function, Lorenz and Zenga curves and related inequality indices. In addition to the well-known stochastic order based on Lorenz curve, the stochastic order based on Zenga curve is considered. Since the new generalized Weibull distribution seems to be suitable to model wealth, financial, actuarial and especially income distributions, these findings are fundamental in the understanding of how parameter values are related to inequality. Also, the estimation of parameters by maximum likelihood and moment methods is discussed. Finally, this distribution has been fitted to United States and Austrian income data sets and has been found to fit remarkably well in compare with the other widely used income models.

KEYWORDS:

• Gini index
• Income distribution
• Lorenz curve
• Odd Weibull distribution
• Zenga curve.

MATHEMATICS SUBJECT CLASSIFCATION:

• 60E15
• 62E15
• 62P20
• 91B82

Acknowledgment

The authors would like to thank the Editor and the referees for very careful reading and valuable comments which greatly improved the paper.

Notes

1 http://www.cesus.gov/hhes/www/income/data/incpovhlth

2 The data set is available from the laeken-package in R software environment.