A comparison of population size estimators under the truncated count model with and without allowance for contaminations.

The purpose of the study is to estimate the population size under a homogeneous truncated count model and under model contaminations via the Horvitz-Thompson approach on the basis of a count capture-recapture experiment. The proposed estimator is based on a mixture of zero-truncated Poisson distributions. The benefit of using the proposed model is statistical inference of the long-tailed or skewed distributions and the concavity of the likelihood function with strong results available on the nonparametric maximum likelihood estimator (NPMLE). The results of comparisons, for finding the appropriate estimator among McKendrick's, Mantel-Haenszel's, Zelterman's, Chao's, the maximum likelihood, and the proposed methods in a simulation study, reveal that under model contaminations the proposed estimator provides the best choice according to its smallest bias and smallest mean square error for a situation of sufficiently large population sizes and the further results show that the proposed estimator performs well even for a homogeneous situation. The empirical examples, containing the cholera epidemic in India based on homogeneity and the heroin user data in Bangkok 2002 based on heterogeneity, are fitted with an excellent goodness-of-fit of the models and the confidence interval estimations may also be of considerable interest.