The one-inflated positive Poisson mixture model for use in population size estimation

The one-inflated positive Poisson mixture model (OIPPMM) is presented, for use as the truncated count model in Horvitz-Thompson estimation of an unknown population size. The OIPPMM offers a way to address two important features of some capture-recapture data: one-inflation and unobserved heterogeneity. The OIPPMM provides markedly different results than some other popular estimators, and these other estimators can appear to be quite biased, or utterly fail due to the boundary problem, when the OIPPMM is the true data-generating process. In addition, the OIPPMM provides a solution to the boundary problem, by labelling any mixture components on the boundary instead as one-inflation.