Article,
Why a time effect often has a limited impact on capture-recapture estimates in closed populations
Canadian Journal of Statistics, 36 (1): 75--84 (March 2008)
DOI: 10.1002/cjs.5550360108
Abstract
The author is concerned with log-linear estimators of the size N of a population in a capture-recapture experiment featuring heterogeneity in the individual capture probabilities and a time effect. He also considers models where the first capture influences the probability of subsequent captures. He derives several results from a new inequality associated with a dispersive ordering for discrete random variables. He shows that in a log-linear model with inter-individual heterogeneity, the estimator N is an increasing function of the heterogeneity parameter. He also shows that the inclusion of a time effect in the capture probabilities decreases N in models without heterogeneity. He further argues that a model featuring heterogeneity can accommodate a time effect through a small change in the heterogeneity parameter. He demonstrates these results using an inequality for the estimators of the heterogeneity parameters and illustrates them in a Monte Carlo experiment
