Inequality measures of weighted generalized beta distribution of the first kind

Generalized beta distribution of the first kind is an important distribution that is properly flexible as an income distribution in economics. in this paper,a new class of weighted generalized beta distribution of the first kind is introduced. besides the common statistical properties,we intend to focus on the economic properties of the distribution,including the measures of inequality such as generalized entropy indices (theil index and the mean log deviation),gini index,pietra index and atkinson index. the maximum likelihood estimation of the parameters of the size-biased generalized beta distribution of the first kind in both grouped and individual data are also included. finally,the weighted generalized beta distribution of the first kind is fitted to the real gross domestic product per capita of 172 countries in 2012 and some its inequality indices are estimated. © 2016 pakistan journal of statistics.