Uncertainty estimation in heterogeneous capture-recapture count data

The Conway-Maxwell-Poisson estimator is considered in this paper as the population size estimator. The benefit of using the Conway-Maxwell-Poisson distribution is that it includes the Bernoulli, the Geometric and the Poisson distributions as special cases and, furthermore, allows for heterogeneity. Little emphasis is often placed on the variability associated with the population size estimate. This paper provides a deep and extensive comparison of bootstrap methods in the capture-recapture setting. It deals with the classical bootstrap approach using the true population size, the true bootstrap, and the classical bootstrap using the observed sample size, the reduced bootstrap. Furthermore, the imputed bootstrap, as well as approximating forms in terms of standard errors and confidence intervals for the population size, under the Conway-Maxwell-Poisson distribution, have been investigated and discussed. These methods are illustrated in a simulation study and in benchmark real data examples.