Estimation of the population size by using the one‐inflated positive Poisson model
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 1s, we propose the one‐inflated positive Poisson model for use as the truncated count distribution in Horvitz–Thompson estimation of the population size.
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