Estimation of parameters in weighted generalized beta distributions of the second kind

This paper applies the class of weighted generalized beta distribution of the second kind (WGB2) as descriptive models for size distribution of income. The properties of WGB2 including mean, variance, coefficient of variation(CV), coefficient of skewness(CS), coefficient of kurtosis(CK) are presented. Other properties including top-sensitive index, bottom-sensitive index, mean logarithmic deviation(MLD) index and Theil index obtained from generalized entropy(GE) are applied in this paper. WGB2 proved to be in the generalized beta-F family of distributions, and maximum likelihood estimation(MLE) is used to obtain the parameter estimates. WGB2 is fitted to U.S. family income (2001-2009) data with different values of the parameters. The empirical results show the length-biased distribution provides the best relative fit.