IJPAM: Volume 82, No. 5 (2013)

THE LEAST UPPER BOUND ON
THE POISSON-BINOMIAL RELATIVE ERROR

K. Teerapabolarn$^1$, A. Boondirek
Department of Mathematics
Faculty of Science
Burapha University
Chonburi, 20131, THAILAND


Abstract. A simple mathematical method is used to determine the least upper bound on the relative error between the binomial cumulative distribution function with parameters $n$ and $p$ and the Poisson cumulative distribution function with mean $\lambda=\frac{np}{q}=\frac{np}{1-p}$. With this upper bound, the Poisson cumulative distribution function with this mean can be used as an estimate of the binomial cumulative distribution function when $p$ is sufficiently small even if $\lambda$ is rather large. By numerical comparison, the upper bound obtained in this study is sharper than those reported in Teerapabolarn [#!KT2!#].

Received: October 25, 2012

AMS Subject Classification: 62E17, 60F05

Key Words and Phrases: binomial distribution, cumulative distribution function, least upper bound, Poisson distribution, relative error

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DOI: 10.12732/ijpam.v82i5.7 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 82
Issue: 5