On certain characterization of normal distribution

A conjecture of Bobkov and Houdré (1995), recently proved by Kwapien et al. (1995), stated that if X and Y are symmetric i.i.d. real random variables such that P((X + Y)/[radical sign]2 > t) [less-than-or-equals, slant] P(X > t) for any t> 0, then X has normal distribution. In this note, we give some generalization of their result with a short and simple proof which can be useful in some other cases.

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Year of publication:	1997
Authors:	Oleszkiewicz, Krzysztof
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 33.1997, 3, p. 277-280
Publisher:	Elsevier
Subject:	Normal distribution

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005223593