Moments of Lorenz Curve and linear measures of inequality

Abstract

The relationship of moments of Lorenz Curve with family of inequality measures $\{{\mathit{I}}_{\mathit{k}}\mathrm{,}\mathit{k}⩾2\}$ is established. Two families of inequality measures, viz., $\{{\mathit{I}}_{\mathit{k}}\mathrm{,}\mathit{k}⩾2\}$ and $\{{\mathit{J}}_{\mathit{k}}\mathrm{,}\mathit{k}⩾1\}$ , are considered as particular cases of general class of linear measures of income inequality with suitable score functions. Each score function defines a particular linear inequality measure and the basic properties of such measures, using some restrictions on score functions are explored. These linear measures of income inequality can also be expressed as linear functions of order statistics. Asymptotic distribution of some of these measures is derived. Tests of significance for one sample and two samples based on these inequality indices are suggested. The simulation work is carried out to find the power of these tests.