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On Littlewood's estimate for the binomial distribution

Published online by Cambridge University Press:  01 July 2016

Brendan D. Mckay
Brendan D. Mckay*
Affiliation:
The Australian National University
*
∗Postal address: Computer Science Department, Australian National University, GPO Box 4, ACT 2601, Australia.
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Abstract

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We correct a theorem of J. E. Littlewood which gives an approximation for the tail of the binomial distribution. We also present several new approximations which are less accurate but have wider scope. One of them gives an estimate with relative error uniformly O(1/σ) over all values of all the parameters, where σ is the standard deviation.

Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 21 , Issue 2 , June 1989 , pp. 475 - 478
Copyright
Copyright © Applied Probability Trust 1989 

References

[1] Bahadur, R. R. (1960) Some approximations to the binomial distribution function. Ann. Math. Statist. 31, 43–54.Google Scholar
[2] Feller, W. (1969) An Introduction to Probability Theory and its Applications, Vol. 1. Wiley, New York.Google Scholar
[3] Littlewood, J. E. (1969) On the probability in the tail of a binomial distribution. Adv. Appl. Prob. 1, 43–72.CrossRefGoogle Scholar
[4] Maple Symbolic Algebra System, Version 4.1 (1987) Symbolic Computation Group, University of Waterloo.Google Scholar