This paper addresses the sampling distribution of two general classes of normative income inequality indices. Specifically, for approximations to the Atkinson-Kolm-Sen index of relative inequality and the Kolm-Blackorby-Donaldson index of absolute inequality, the paper provides consistent estimators based on a random sample of income microdata and establishes their asymptotic normality. Asymptotic variance-covariance expressions are obtained that provide for distribution-free statistical inference on these measures in a straightforward fashion. The paper thus extends the principles of statistical inference to current classes of normative inequality measures and to Atkinson's equally distributed income measure, using a general approximation approach. An example using Canadian family income microdata illustrates the technique.