Inequality in the relative differential sense with continuous distributions

Existing literature has studied the relative differential inequality (RDI) concept as an inequality comparison for discrete distributions, where RDI dominance occurs if there is Lorenz dominance between the distributions for all subsets of individuals of corresponding rank. The paper investigates RDI in the context of continuous distributions, providing continuous counterparts to existing discrete results, and others, including discussion of the uniform, Pareto and log-normal families of continuous distributions. The usefulness of RDI for comparative static analysis in theoretical economic models based on continuous distributions is indicated.