On the bias of the Hoover index estimator: Results for the gamma distribution

TL;DR

This paper investigates the finite-sample bias of the Hoover index estimator, deriving explicit bias formulas for gamma distributions and demonstrating how bias varies with sample size and distribution.

Contribution

It provides a unified analytical framework for the bias of the Hoover index estimator applicable to both continuous and discrete populations, with explicit bias expressions for gamma distributions.

Findings

The Hoover index estimator is generally biased in finite samples.

Bias magnitude depends on the underlying distribution and sample size.

Simulation results illustrate the bias behavior across different scenarios.

Abstract

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.