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An asymptotic expansion for the tail of a binomial distribution and its application in queueing theory

Published online by Cambridge University Press:  14 July 2016

P. J. Brockwell
P. J. Brockwell*
Affiliation:
Australian National University
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Abstract

An asymptotic expansion is derived for Sr(n)/Tr(n), where r and n are integers, and . Bounds for the remainder after kterms of the expansion are obtained and it is shown how the expansion may be applied in hypothesis testing and the study of the transient behaviour of a queue with batch arrivals.

Type
Short Communications
Information
Journal of Applied Probability , Volume 1 , Issue 1 , June 1964 , pp. 161 - 167
Copyright
Copyright © Applied Probability Trust 1964 

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References

[1] Brockwell, P. J. (1963) The transient behaviour of a queue with batch arrivals. J. Aust. Math. Soc. 3, 241–248.Google Scholar
[2] Bahadur, R. R. (1960) Some approximations to the binomial distribution function. Ann. Math. Statist. 31, 43–54.Google Scholar
[3] Robbins, H. (1955) A remark on Stirling's formula, Amer. Math. Monthly 62, 26–29.Google Scholar
[4] Tables of the Cumulative Binomial Distribution (1955) Harvard University Press.Google Scholar