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Unbiased estimation in new Gini index extensions under gamma distributions
Roberto Vila, Helton Saulo
https://arxiv.org/abs/2506.00666 https://

Unbiased estimation in new Gini index extensions under gamma distributions
In this paper, we propose two new flexible Gini indices (extended lower and upper) defined via differences between the $i$-th observation, the smallest order statistic, and the largest order statistic, for any $1 \leqslant i \leqslant m$. For gamma-distributed data, we obtain exact expectations of the estimators and establish their unbiasedness, generalizing prior works by [Deltas, G. 2003. The small-sample bias of the gini coefficient: Results and implications for empirical research. Review of…