Estimation of the population size by using the one-inflated positive Poisson model

摘要

In population size estimation, many capture-recapture-type data exhibit a preponderance of '1'-counts. This excess of 1s can arise as subjects gain information from the initial capture that provides a desire and ability to avoid subsequent captures. Existing population size estimators that purport to deal with heterogeneity can be much too large in the presence of 1 -inflation, which is a specific form of heterogeneity. To deal with the phenomena of excess 1 s, we propose the one-inflated positive Poisson model for use as the truncated count distribution in Horvitz-Thompson estimation of the population size.