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, (Formula presented.), and the number of animals or species that have been observed (Formula presented.) and more than (Formula presented.) 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 (Formula presented.) 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 (Formula presented.) is superior to censoring at (Formula presented.).