Gamma family characterization and an alternative proof of Gini estimator unbiasedness
By: Roberto Vila
In this paper, we derive a general representation for the expectation of the (upward adjusted) Gini coefficient estimator in terms of the Laplace transform of the underlying distribution. This representation leads to a characterization of the gamma family within the class of nonnegative scale families, based on a stability property of exponentially tilted distributions. As an application, we provide an alternative proof of the unbiasedness of the Gini coefficient estimator under gamma populations.
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