IJPAM: Volume 98, No. 1 (2015)

NEGATIVE BINOMIAL APPROXIMATION TO
THE BETA BINOMIAL DISTRIBUTION

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


Abstract. This paper determines a bound on the approximation of the beta binomial distribution with parameters $n$, $\alpha$ and $\beta$ by a negative binomial distribution with parameters $\alpha$ and $\frac{\alpha+\beta}{\alpha+\beta+n}$. With this bound, it is indicated that the beta binomial distribution can be well approximated by the negative binomial distribution when $\beta$ is large.

Received: August 18, 2014

AMS Subject Classification: 62E17, 60F05

Key Words and Phrases: beta binomial distribution, negative binomial approximation, Stein's method, $w$-function associated with the beta binomial random variable

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DOI: 10.12732/ijpam.v98i1.5 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: 2015
Volume: 98
Issue: 1
Pages: 39 - 43


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