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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.01659 |
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| _version_ | 1866909599841386496 |
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| author | Vila, Roberto Saulo, Helton |
| author_facet | Vila, Roberto Saulo, Helton |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01659 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An unbiased estimator of a novel extended Gini index for gamma distributed populations Vila, Roberto Saulo, Helton Methodology 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. |
| title | An unbiased estimator of a novel extended Gini index for gamma distributed populations |
| topic | Methodology |
| url | https://arxiv.org/abs/2505.01659 |