On two occasions capture and recapture designs: Comparing and discussing some estimators

SUMMARY Capture and recapture designs with only two occasions are still being used in a variety of situations especially in Epidemiological studies. Usually, the well-known Lincoln-Petersen (1896,1930) estimator is used to estimate the population size. Because only two occasions are being used some concern is devoted to the reliability of the final estimate. In this paper we will address the problem by comparing the Lincoln-Petersen estimator with three others proposed in the literature: Chapman (1951), Bailey (1951) and the stepwise Bayesian estimators (Mingoti,2000). By using a mathematical relationship it will be shown that the Bayes estimator has an expected value smaller than Lincoln-Petersen's and higher variability unless the sample sizes are large in which case the variability is almost the same. The simulation study shows that for small sample fractions, in both capture and recapture stages, the Bayes estimator has a better performance, but for larger sample fractions the Bayes estimator had a similar or worse performance than the other three. Chapman and Bailey are good alternatives in several cases.