Population size estimation and heterogeneity in capture-recapture data: a linear regression estimator based on the Conway-Maxwell-Poisson distribution

The purpose of the study is to estimate the population size under a truncated count model that accounts for heterogeneity. The proposed estimator is based on the Conway–Maxwell–Poisson distribution. 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. Parameter estimates can be obtained by exploiting the ratios of successive frequency counts in a weighted linear regression framework. The results of the comparisons with Turing’s, the maximum likelihood Poisson, Zelterman’s and Chao’s estimators reveal that our proposal can be beneficially used. Furthermore, our proposal outperforms its competitors under all heterogeneous settings. The empirical examples consider the homogeneous case and several heterogeneous cases, each with its own features, and provide interesting insights on the behavior of the estimators.