IJPAM: Volume 87, No. 4 (2013)

A BOUND ON THE POISSON
BINOMIAL-POISSON RELATIVE ERROR

K. Teerapabolarn
Department of Mathematics
Faculty of Science
Burapha University
Chonburi, 20131, THAILAND


Abstract. We use the Stein-Chen method to determine a bound on the relative error between the Poisson binomial distribution function with parameter $\textbf{p}=(p_1,...,p_n)$ and the Poisson distribution function with mean $\lambda=\sum_{i=1}^n\frac{p_i}{1-p_i}$. With this bound, the Poisson distribution function with this mean can be used as an estimate of the Poisson binomial distribution function whenever all $p_i$ are small.

Received: May 7, 2013

AMS Subject Classification: 62E17, 60F05, 60G50

Key Words and Phrases: distribution function, Poisson distribution, Poisson binomial distribution, relative error, Stein-Chen method

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DOI: 10.12732/ijpam.v87i4.4 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: 87
Issue: 4