Generalization of Simmons' theorem

If Xm has a binomial distribution , n[greater-or-equal, slanted]3, with 0<2m<n, the theorem of Simmons asserts that P(Xm<m)>P(Xm>m); if Xm has a Poisson distribution , we have a similar result but, furthermore, Teicher proved that both sequences P(Xm<m) and P(Xm>m) are increasing. The aim of this note is to give a simple proof of these results and to extend them to geometric and negative binomial distributions.

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Year of publication:	2007
Authors:	Perrin, Olivier ; Redside, Edmond
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 77.2007, 6, p. 604-606
Publisher:	Elsevier
Keywords:	Beta Gamma and negative binomial distributions Simmons' theorem

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

Persistent link: https://www.econbiz.de/10005138306