Performance of confidence intervals for the population size in capture-recapture experiment under inverse sampling with replacement

Lui [Five confidence intervals of the closed population size in the capture-recapture problem under inverse sampling with replacement. Biom J. 2004;46:474-480] considered five confidence intervals for the closed population size in a two-sample capture-recapture experiment under inverse sampling with replacement in the recapture phase. The results of his Monte Carlo study indicated that the exact confidence intervals and those based on chi(2)-approximation perform very well. In this paper, we consider three other methods of interval estimation including the bootstrap, likelihood ratio and Jeffreys prior approaches. A Monte Carlo simulation is carried out to evaluate the performance of these intervals together with those based on existing methods in terms of the coverage probability, error rates and standardized average length. Our results show that confidence intervals based on Wald statistics, logarithmic transformation, and bootstrap methods are inappropriate, having coverage probabilities less than the desired nominal level. Also, the exact confidence intervals and those based on chi(2)-approximation are not invariant with respect to the proportion of marked individuals in the capture phase, say p. When p is chosen to be small-to-moderate, the likelihood ratio method is preferred, since it gives confidence intervals with shorter length from among all methods that provide the coverage probability close to the desired nominal level. Overall, the Jeffreys method appears to be more robust than other competitors, providing intervals with nearest coverage probabilities to the desired nominal level and with balanced non-coverage rates.