Bayesian Estimation of n in a Binomial Distribution
CENTER FOR NAVAL ANALYSES ALEXANDRIA VA STRIKE AND AMPHIBIOUS WARFARE RESEARCH DEPT
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Let X Sub 1,X Sub 2,...,X, be a random sample of size r from a binomial distribution bn, p. Let x Sub 1,x Sub 2,...,x Sub r, be r-observed success counts. A method has been developed to estimate the total number of trials n from a Bayesian perspective when the probability of success p is either known or unknown. The prior distribution for n is assumed to be the discrete uniform distribution. In the case when p is unknown, p is assumed to have a beta prior distribution. The estimate for n is then the mode of the posterior distribution. Additionally, guidelines for selecting shape parameters for the beta distributions are discussed.
- Statistics and Probability
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