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arXiv · 2505.01659

An unbiased estimator of a novel extended Gini index for gamma distributed populations

Roberto Vila·Helton Saulo
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Abstract

In this paper, we introduce a novel flexible Gini index, referred to as the extended Gini index, which is defined through ordered differences between the $j$th and $k$th order statistics within subsamples of size $m$, for indices satisfying $1 \leqslant j \leqslant k \leqslant m$. We derive a closed-form expression for the expectation of the corresponding estimator under the gamma distribution and prove its unbiasedness, thereby extending prior findings by \cite{Deltas2003}, \cite{Baydil2025}, and \cite{Vila2025}. A Monte Carlo simulation illustrates the estimator's finite-sample unbiasedness. A real data set on gross domestic product (GDP) per capita is analyzed to illustrate the proposed measure.

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Roberto Vila, Helton Saulo. 2025-05-03. An unbiased estimator of a novel extended Gini index for gamma distributed populations. https://arxiv.org/abs/2505.01659

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