Comparison of concentration for several families of income distributions

In this paper, we consider the comparison of parametric families of income distributions in terms of inequality and relative deprivation, which are two important aspects for understanding the concentration of incomes in a population. Based on inequalities of their parameters, we give sufficient, and in some cases necessary, conditions to show when a parametric model exhibits more deprivation and inequality than another parametric model. These comparisons are carried out in terms of the starshaped, expected proportional shortfall, and Lorenz orders.