The $m$th Gini index estimator: Unbiasedness for gamma populations

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