A Note on Inequality Measures for Mixtures of Double Pareto-Lognormal Distributions

Formulas are derived for the Gini, Theil and Pietra coefficients for a population-weighted mixture of double Pareto-lognormal distributions; they are applied to South America for two years. Results are also provided for the special case Pareto-lognormal and lognormal distributions. The formulas are useful for measuring regional or global inequality in large-scale projects that utilise double Pareto-lognormal distributions or their special cases.