The Hoover index is a widely used measure of inequality with an intuitive interpretation, yet little is known about the finite-sample properties of its empirical estimator. In this paper, we derive a simple expression for the expected value of the Hoover index estimator for general non-negative populations, based on Laplace transform techniques and exponential tilting. This unified framework applies to both continuous and discrete distributions. Explicit bias expressions are obtained for gamma population, showing that the estimator is generally biased in finite samples. Numerical and simulation results illustrate the magnitude of the bias and its dependence on the underlying distribution and sample size.

翻译：胡佛指数是一种广泛使用的不平等度量指标，具有直观的解释意义，但其经验估计量的有限样本性质却鲜为人知。本文基于拉普拉斯变换技术和指数倾斜方法，推导出一般非负总体下胡佛指数估计量期望值的简洁表达式。这一统一框架适用于连续分布与离散分布。针对伽马总体获得了显式的偏差表达式，表明该估计量在有限样本下通常存在偏差。数值与模拟结果展示了偏差的大小及其对底层分布与样本量的依赖关系。