This paper presents consistent estimators for some important in- come inequality indexes. The empirical distribution function has an impor- tant role in finding these estimators which under weak conditions are asymp- totical normal. Based on asymptotic normality, it is possible to make some inferential statistics such as test hypotheses about inequality indexes and con- struct confidence intervals for them. To estimate the mean and variance of the studied estimators, bootstrap, jackknife, linearization method and theory of U-statistics are proposed.

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