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This paper presents the results of a systematic numerical investigation of the comparative accuracy of several approximations to the cumulative binomial distribution. The approximations studied include the normal, arcsine, Poisson, and six others. Two of the little-known approximations were found to be extremely good: the Poisson Gram-Charlier when the probability p is fairly small, and the Camp-Paulson approximation almost everywhere.
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Morton S. Raff (1956) studied this question.
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