An extension of Chao’s estimator of population size based on the first three capture frequency counts

A new estimator for estimating the size of an elusive target population is presented using frequency counts from capture–recapture sampling. The proposed estimator is developed by extending the idea of Chao’s estimator using monotonicity of ratios of neighbouring frequency counts under a specific Poisson mixture sampling framework, the Poisson–Gamma mixture or negative binomial. The new estimator is achieved using a simple linear model on the basis of the log-ratio of neighbouring frequency counts as dependent variable which is valid under the Poisson–Gamma mixture. A simulation study is provided to study the performance of the proposed estimator under a variety of heterogeneous Poisson capture probabilities. Confidence interval estimation is done by means of an approximating normal approach and a modified bootstrap method, and was found to perform well. A variety of real data sets were also examined in order to illustrate the use of the proposed method.