Measuring group disadvantage with indices based on relative distributions

A long literature on between-group inequality in Social Science and Statistics has developed statistical tools (indices and tests) in order to measure the extent of inequality of opportunity or, more narrowly, gender inequality. In this paper I propose a family of new indices which measure and are sensitive to inequality between pairs of groups whenever that inequality implies disadvantage for a group of concern. The indices are based on cumulative relative distributions and the disadvantage is captured through differences between the quantiles of the distributions. The indices are advocated to study topics like gender inequality and are suitable for continuous variables. With a random transformation the indices can also be applied to discrete variables. The indices are put into action to study gender inequality in Chile over several dimensions of well-being. I find that gender differences are most detrimental to women in dimensions of earnings, dignity and life satisfaction.