An Approximation Of The Cumulative Binomial Probability Distribution
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An Approximation of the Cumulative Binomial Probability Distribution
The cumulative binomial distribution B(x;n, p) is the probability of x or less successes in n trials with p the probability of success in a single trial. There is no practical and concise procedure for calculating the B(x;n, p) for large values of n. There is no brief tabular presentation of the B(x;n, p) as there is for the cumulative Poisson and normal distributions. The cumulative binomial distribution is operationally defined, and the currently used approximations to it are discussed. An asymptotic expansion of the distribution of a sample sum is used to produce an approximation of the cumulative binomial probability distribution with the desired accuracy of three decimal places.