The mth Gini index estimator: Unbiasedness for gamma populations

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 et al. (2024), for gamma-distributed populations, extending and generalizing the key finding of Baydil et al. (2025). An illustrative Monte Carlo simulation study is performed to numerically check that our implementation recovers the theoretical unbiasednes of the sample mth Gini index estimator in finite samples.