Abstract
Abstract The need to estimate the sample size parameter n in the binomial distribution arises in many practical problems, such as estimating wildlife population sizes based on sample counts. Attempts to find reasonable estimators can be traced back to the early 1900s, when the method of moments estimator was proposed. But the method of moments estimator, as well as the maximum likelihood estimator, suffers serious shortcomings in terms of performance, not the least of which is a highly unstable behavior. Following a few examples and a brief history of the problem, this entry details some of the difficulties that arise when estimating n , and presents the results of attempts that have been made to overcome those difficulties either by modifying the method of moments or maximum likelihood estimator, or adopting a Bayesian approach.
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