Measures of income inequality are used for modelling and analysis of income data. In this paper, we present various income inequality measures in the quantile set up. We also introduce quantile version of well known dullness property. The interrelationships among these measures are investigated. The monotonic behaviour of income inequality measures are discussed. We also develop new quantile functions useful for income analysis. Various applications of the measures are discussed.
Sankaran et al. (Tue,) studied this question.