The mth Gini index estimator: Unbiasedness for gamma populations

2025/04/27 by Roberto Vila, Vila, Roberto, Helton Saulo +1 · 3 citations
Mathematics · #Census and Population Estimation #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference

paper · pdf · doi:10.48550/arxiv.2504.19381

openalex publication_date 2025/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper establishes the theoretical result that the sample mth Gini index is an unbiased estimator of the population mth Gini index, introduced by Gavilan-Ruiz (2024), for gamma-distributed populations. An illustrative Monte Carlo simulation study confirms the unbiasedness of the sample mth Gini index estimator in finite samples.

Cited by

• On the bias of the Gini estimator: Poisson and geometric cases, a characterization of the gamma family, and unbiasedness under gamma distributions
• Bias in estimating Theil, Atkinson, and dispersion indices for gamma mixture populations
• Unbiased estimation in new Gini index extensions under gamma distributions, with application to real income data

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