An Entropy Transformed Pareto Distribution for Measuring Wealth Inequality

In this study, an Entropy Transformed Pareto Distribution (EnTrPD) was proposed to provide improved flexibility in modelling heavy-tailed behavior observed in data, and was subsequently applied to assess wealth inequalities in Nigeria using quarterly Gross Domestic Product (GDP) data. The derived properties of the distribution include <inline-formula> <tex-math notation="LaTeX">$n^{\mathrm {th}}$ </tex-math></inline-formula> moment, characteristic function, mean, and variance. The model parameters were estimated using five parameter estimation techniques: the maximum likelihood, least squares, weighted least square, Cramer-von Mises, and Anderson Darling methods. Through simulation, the model was validated to be consistent with large sample inference, and it showed that all five estimators yielded estimates that converged to the true parameter value as sample size increased, reflecting consistency, high accuracy, and stability. On application to GDP data, the results showed that the classical Pareto distribution overestimated inequality. Particularly in the upper tail, it produce inflated Gini coefficients and extreme top-income shares. However, the EnTrPD yielded inequality measures that reflected the Nigerian economy, with Gini coefficients ranging from 0.35 to 0.56 with stable Atkinson and Generalized Entropy indices. In addition, the Lorenz curve and density analyses confirmed that the EnTrPD effectively captured heavy-tail behavior and extreme wealth concentrations without exaggeration, demonstrating its superiority over the classical Pareto method in modelling heavy-tailed economic distributions and assessing inequality.