IJPAM: Volume 87, No. 4 (2013)

A NON-UNIFORM BOUND ON THE POINT METRIC OF
POISSON BINOMIAL AND BINOMIAL DISTRIBUTIONS

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


Abstract. We use Stein's method to determine a non-uniform bound on the point metric of the Poisson binomial distribution with parameter $\textbf{p}=(p_1,...,p_n)$ and the binomial distribution with parameters $n'$ and $p'$, where $n'$ is the integral part of $\left\{\frac{\left(\sum_{i=1}^np_i\right)^2}{\sum_{i=1}^np_i^2}+\frac{1}{2}\right\}$ and $p'=\frac{1}{n'}\sum_{i=1}^np_i$. The bound in this study is more appropriate for measuring the accuracy of the approximation.

Received: May 7, 2013

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

Key Words and Phrases: binomial distribution, non-uniform bound, Poisson binomial distribution, point metric, Stein's method

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DOI: 10.12732/ijpam.v87i4.5 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