A Comparison ofnEstimators for the Binomial Distribution

Abstract

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.