统一霍夫曼指数和基尼指数：分析、偏差和计算方面
Unifying the Hoover and Gini indices: Analytical, bias, and computational aspects
AI总结：
本文提出了一种新的不平等指数家族，连接霍夫曼指数和基尼系数，通过分析性质和统计方法展示了其理论和应用价值。
摘要：
我们提出了一种新的不平等指数家族，连接霍夫曼指数和基尼系数。该度量定义为标准化的凸组合偏差和成对差异的绝对值的期望值，提供了这两种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、连续性和符合皮戈-达尔顿转移原则。推导了分析表达式，允许在伽马分布下显式评估，并导致涉及不完整伽马函数的闭式表达。从统计学角度来看，我们研究了插件估计器，得到了其期望的一般表达式以及在伽马总体下的显式偏倚公式。模拟结果表明，有限样本性能良好，样本量增加时偏倚和均方误差减小。对人均GDP数据的实证应用展示了所提出指数作为不平等分析灵活工具的实用性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
