Estimation of quantile inequality curves and measures is considered in a parametric model based on grouped data. The unknown parameters of the distribution are estimated using the minimum divergence method, using various $φ$-divergences. The consistency of the plug-in estimators of the inequality curves and measures and the asymptotic normality of the indices estimators are proved. In a simulation study, the methods are verified and compared in terms of the accuracy of the estimation. The practical applications of the proposed methods are illustrated by the analysis of two real data sets.

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