Characterizations of the Normal and the Gamma distributions

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1973 English Publisher:Springer Science and Business Media LLCJournal:Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, volume 26, pages 335-344 (issn: 0044-3719, eissn: 1432-2064,

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Authors: Bondesson, Lennart;

doi: 10.1007/bf00534897

Characterizations of the Normal and the Gamma distributions

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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.

Related Organizations

Mittag-Leffler Institute
Sweden
Lund University
Sweden
Royal Swedish Academy of Sciences
Sweden

Keywords

Probability distributions: general theory

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