IJPAM: Volume 93, No. 6 (2014)
POISSON APPROXIMATION FOR INDEPENDENT
NEGATIVE BINOMIAL RANDOM VARIABLES
NEGATIVE BINOMIAL RANDOM VARIABLES
K. Teerapabolarn
Department of Mathematics
Faculty of Science
Burapha University
Chonburi, 20131, THAILAND
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
, where
and
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
is small.
Received: December 25, 2013
AMS Subject Classification: 62E17, 60F05, 60G50
Key Words and Phrases: negative binomial distribution, Poisson distribution, Poisson approximation, -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
