On a new Pareto-type distribution with applications in the study of income inequality and risk analysis

Abstract

A recent paper published in this journal (Bourguignon et al., 2016) introduces and studies a new Pareto-type distribution, deriving some of its probabilistic and inferential properties. In this paper, we obtain additional and important properties of this distribution and derive simpler expressions for relevant inequality indices and risk measures. One important feature of this distribution is that many of these expressions are simple functions of the incomplete beta function. Using this result, we obtain closed expressions for the moments and for several inequality measures including the Gini index and the Lorenz curve, the Donaldson–Weymark–Kakwani index, the Pietra index and the generalized entropy measures. Basic risk measures are also obtained. Finally, empirical applications with real income data are given.