Abstract
We show that the conventional income inequality indexes assess income inequality incorrectly because of three problems. The unequally distributed (UD) income-based approach solves the problems, decomposes income inequality into two kinds of departure from equality, and provides two indexes. The comprehensive assessment of income inequality requires the integration of two kinds of departure. This paper proposes the relative UD (RUD) income-based approach. The RUD income-based approach combines the cumulative distribution function and quantile function of the RUD income and produces a new index integrating two kinds of departure. We investigate the properties of the new index and demonstrate its applicability through example income distributions.