IJPAM: Volume 93, No. 6 (2014)

POISSON APPROXIMATION FOR INDEPENDENT
NEGATIVE BINOMIAL RANDOM VARIABLES

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


Abstract. We give a bound for the total variation distance between the distribution of a sum of independent negative binomial random variables and an appropriate Poisson distribution with mean $\sum_{i=1}^n\frac{r_iq_i}{p_i}$, where $r_i$ and $p_i=1-q_i$ are parameters of each negative binomial distribution. It is indicated that the distribution of the sum can be approximated by the Poisson distribution with this mean when each $r_iq_i$ is small.

Received: December 25, 2013

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

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

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DOI: 10.12732/ijpam.v93i6.2 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: 779 - 781

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