We propose a new family of inequality indices that bridges the Hoover index and the Gini coefficient. The measure is defined as the normalized expected absolute value of a convex combination of deviations from the mean and pairwise differences, providing a continuous interpolation between these two classical indices. We establish key theoretical properties, including scale invariance, boundedness, continuity, and compliance with the Pigou-Dalton transfer principle. Analytical representations are derived, allowing explicit evaluation under gamma distributions and leading to closed-form expressions involving incomplete gamma functions. From a statistical perspective, we study the plug-in estimator, obtaining a general expression for its expectation and explicit formulas for its bias under gamma populations. Simulation results indicate good finite-sample performance, with decreasing bias and mean squared error as the sample size increases. An empirical application to GDP per capita data illustrates the practical usefulness of the proposed index as a flexible tool for inequality analysis.

翻译：本文提出了一类新的不平等指数族，该指数族在胡佛指数与基尼系数之间建立了桥梁。该度量定义为均值偏差与成对差异的凸组合的归一化期望绝对值，提供了这两个经典指数之间的连续插值。我们建立了关键的理论性质，包括尺度不变性、有界性、连续性以及符合庇古-道尔顿转移原则。我们推导了解析表示形式，使得在伽马分布下能够进行显式评估，并得出涉及不完全伽马函数的闭式表达式。从统计学角度，我们研究了插件估计量，得到了其期望的一般表达式以及伽马总体下偏差的显式公式。模拟结果表明，随着样本量的增加，偏差和均方误差减小，具有良好的有限样本性能。对人均GDP数据的实证应用说明了所提指数作为不平等分析灵活工具的实际效用。