Estimation of Lorenz, Schotz and Champernowne-Pareto Measures of Income Inequality Relative to the Poverty Gab-Ratio for Achieving Social Equality

The fundamental goal of the paper is to introduce an adequate mathematical solution for achieving social equality through analyzing the relation between income distribution curve and poverty line of a society. This relation would determine how many incomes of population groups fall below poverty line and identify their position among low and medium income classes. Hence some relative measures of income inequality derived from three functional curves of income graduation, namely Lorenz, Schotz and Champernowne-Pareto have been analyzed. Meantime three relative indices of deviations of income disparities from poverty line are estimated. Then an adequate treatment to shift these gaps, are obtained to achieve the social and income equality. Both of the two groups of income and poverty measures are estimated from the Egyptian family data 2008/2009 by fitting the three income curves as well as the poverty line to the household income and expenditure. Hence, some specific statements about poverty rate and the income percentages needed to be transformed from the rich to the poor people have been determined.