IJPAM: Volume 95, No. 1 (2014)

NEGATIVE BINOMIAL APPROXIMATION TO
THE GENERALIZED HYPERGEOMETRIC DISTRIBUTION

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


Abstract. This paper uses Stein's method and the $w$-function associated with the generalized hypergeometric random variable to determine a bound for the total variation distance between the generalized hypergeometric distribution with parameters $\alpha$, $\beta$ and $N$ and the negative binomial distribution with parameters $r=\beta+1$ and $p=1-q=\frac{\alpha+\beta+2}{\alpha+\beta+N+1}$. In view of this bound, it is observed that the desired result gives a good negative binomial approximation when $\alpha$ is large.

Received: April 23, 2014

AMS Subject Classification: 62E17, 60F05

Key Words and Phrases: generalized hypergeometric distribution, negative binomial approximation, total variation distance, Stein's method

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DOI: 10.12732/ijpam.v95i1.11 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: 95
Issue: 1
Pages: 99 - 103


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