A Note onNEstimators for the Binomial Distribution

Consider k success counts from a binomial distribution with unknown N and success probability p. We examine the problem of estimating N. By integrating the likelihood for N and p over a beta density for p, we obtain the beta-binomial distribution resulting in stable and reasonably efficient estimators of N, which compare favorably with and are often better than the estimates introduced by Olkin et al. (1981).