A Non-Parametric Estimation Method of the Population Size in Capture-Recapture Experiments With Right Censored Data

We present a new non-parametric approach for estimating the total number of animals or species when we only have information on the number of animals or species that have been observed once, twice, $\dots$, and the number of animals or species that have been observed $r$ and more than $r$ times. The approach, like the Chao estimator, gives a lower bound on population size while also providing bootstrap confidence intervals. We conducted simulations to compare our estimator to other competing ones in special scenarios with $r=2$ and 3 and found that it performed quite well. In the case of uncensored samples, we analyze which censoring point is preferable in specific examples, as well as when censoring at $r=3$ is superior to censoring at $r=2$.