Two Tunable Gini-Type Measures with U-Statistic Estimation: Theory, Simulation, and an Empirical Application to GDP per Capita in the Americas

We introduce two families of inequality measures, $G_p$ and $H_q$, that converge to the classical Gini coefficient as $p,q\to \mathrm{\infty }$. The tuning parameters $p>1$ and $q>0$ regulate the influence of disparities between observations. For each index we derive closed-form $U$-statistic plug-in estimators and establish strong consistency and asymptotic normality under mild moment conditions. A Monte Carlo study assesses finite-sample behavior across $(n,p,q)$, and an empirical illustration with GDP per capita in the Americas shows how the tuning parameters influence the measure of inequality.