Maximum Likelihood Estimates for the Schnabel Census with Plants

Abstract

We consider a generalization of the Schnabel census in which a known number of planted individuals is added to the target population before sampling commences. We derive the distribution of the number of distinct target individuals seen after drawing samples of predetermined size, and prove that the ensuing likelihood function is unimodal. We obtain the maximum likelihood estimator, together with its asymptotic moments, and investigate its small sample properties computationally. Two approaches for obtaining confidence intervals based on maximum likelihood estimates are presented and compared.