Abstract
The Normal and the Gamma distribution, properly translated, are characterized by a uniformly minimum variance property of the sample mean. In fact, we answer in particular a question asked by Kagan in 1966. Also an optimality property of the sample variance is proved to characterize the Normal distribution.
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Bondesson, L. Characterizations of the Normal and the Gamma distributions. Z. Wahrscheinlichkeitstheorie verw Gebiete 26, 335–344 (1973). https://doi.org/10.1007/BF00534897
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DOI: https://doi.org/10.1007/BF00534897