Estimating the number, n, of trials, given a sequence of independent success counts obtained by replicating the n-trial experiment is less studied and a considerably harder problem than estimating p for the binomial distribution. Both the method of moments and the maximum likelihood estimators of n are considered. When p is unknown and small, while n is large, both estimators become highly unstable. Stabilized versions of these estimators are proposed, and their performance is described in terms of results obtained by simulation.
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Olkin et al. (1981) studied this question.
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