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October, 1971 On the Convergence of Binomial to Poisson Distributions
Gordon Simons, N. L. Johnson
Ann. Math. Statist. 42(5): 1735-1736 (October, 1971). DOI: 10.1214/aoms/1177693172


Following the work of Poisson (1837), there has been considerable practical and theoretical interest in how well the Poisson distribution approximates the binomial distribution. The approximation, which was initially suggested by a limit theorem (see (1) below), has been shown in numerical examples to be very good for certain binomial parameters within a useful range. (See Feller (1950), page 143.) Subsequently, (nonasymptotic) theoretical results have confirmed the approximation's accuracy. (See (2.1) and (2.2) below.) The purpose of this note is to demonstrate, with an elementary argument, that the binomial distributions converge very strongly to the Poisson distributions.


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Gordon Simons. N. L. Johnson. "On the Convergence of Binomial to Poisson Distributions." Ann. Math. Statist. 42 (5) 1735 - 1736, October, 1971.


Published: October, 1971
First available in Project Euclid: 27 April 2007

zbMATH: 0235.60033
MathSciNet: MR345171
Digital Object Identifier: 10.1214/aoms/1177693172

Rights: Copyright © 1971 Institute of Mathematical Statistics


Vol.42 • No. 5 • October, 1971
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