Estimating the Complete Sample Size from an Incomplete Poisson Sample

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Abstract
Maximum likelihood estimators and a modified maximum likelihood estimator are developed for estimating the zero class from a truncated Poisson sample when the available sample size itself is a random variable. All the estimators considered here are asymptotically equivalent in the usual sense; hence their asymptotic properties are investigated in some detail theoretically as well as by making use of Monte Carlo experiments. One modified estimator appears to be best with respect to the chosen criteria. An example is given to illustrate the results obtained.

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