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August, 1965 On the Number of Successes in Independent Trials
S. M. Samuels
Ann. Math. Statist. 36(4): 1272-1278 (August, 1965). DOI: 10.1214/aoms/1177699998

Abstract

The distribution of the number of successes in independent trials is shown to be bell-shaped of every order. The most likely number of successes is "almost uniquely" determined from the mean number and from the mean plus the largest and smallest probability of success on any trial. Bounds on the distribution function of the number of successes are obtained and extended to an infinite number of trials, including the Poisson distribution.

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S. M. Samuels. "On the Number of Successes in Independent Trials." Ann. Math. Statist. 36 (4) 1272 - 1278, August, 1965. https://doi.org/10.1214/aoms/1177699998

Information

Published: August, 1965
First available in Project Euclid: 27 April 2007

zbMATH: 0156.40506
MathSciNet: MR179825
Digital Object Identifier: 10.1214/aoms/1177699998

Rights: Copyright © 1965 Institute of Mathematical Statistics

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Vol.36 • No. 4 • August, 1965
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