The Annals of Probability

On the Convergence of Poisson Binomial to Poisson Distributions

Louis H. Y. Chen

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Abstract

It is well known that under certain conditions, binomial distributions converge to Poisson distributions. Simons and Johnson (1971) showed that the convergence is actually much stronger than in the usual sense. In this note the author shows that the result of Simons and Johnson is also true for Poisson binomial distributions which include binomial distributions as special cases.

Article information

Source
Ann. Probab., Volume 2, Number 1 (1974), 178-180.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996766

Digital Object Identifier
doi:10.1214/aop/1176996766

Mathematical Reviews number (MathSciNet)
MR370693

Zentralblatt MATH identifier
0276.60024

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 62E99: None of the above, but in this section

Keywords
Poisson distribution Poisson binomial distribution Poisson convergence

Citation

Chen, Louis H. Y. On the Convergence of Poisson Binomial to Poisson Distributions. Ann. Probab. 2 (1974), no. 1, 178--180. doi:10.1214/aop/1176996766. https://projecteuclid.org/euclid.aop/1176996766


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