IJPAM: Volume 93, No. 6 (2014)

POISSON APPROXIMATION FOR
INDEPENDENT BINOMIAL RANDOM VARIABLES

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


Abstract. This paper gives a bound for the total variation distance between the distribution of a sum of independent binomial random variables and an appropriate Poisson distribution with mean $\sum_{i=1}^nm_ip_i$, where $m_i$ and $p_i=1-q_i$ are parameters of each binomial distribution. With this bound, it is indicated that the distribution of the sum can be approximated by the Poisson distribution when each $m_ip_i$ is small.

Received: December 25, 2013

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

Key Words and Phrases: binomial distribution, Poisson distribution, Poisson approximation, $w$-function

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DOI: 10.12732/ijpam.v93i6.1 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: 2014
Volume: 93
Issue: 6
Pages: 775 - 777

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).