Estimation of inequality indices of the cumulative distribution function

•We study inequality indices of the cumulative distribution function.•We derive their large sample distribution in a general framework.•We provide a method for obtaining analytic standard errors.•We give examples in the context of two families of inequality indices.•We provide an application using Egyptian demographic and health data.

Inequality indices for self-assessed health and life satisfaction are typically constructed as functions of the cumulative distribution function. We present a unified methodology for the estimation of the resulting inequality indices. We also obtain explicit standard error formulas in the context of two popular families of inequality indices that have emerged from this literature.