Capture-recapture modelling for zero-truncated count data allowing for heterogeneity

Capture-recapture modelling is a powerful tool for estimating an elusive target population size. This thesis proposes four new population size estimators allowing for population heterogeneity. The first estimator is developed under the zero-truncated of generalised Poisson distribution (ZTGP), called the MLEGP. The two parameters of the ZTGP are estimated by using a maximum likelihood with the Expectation-Maximisation algorithm (EM algorithm).The second estimator is the population size estimator under the zero-truncated Conway-Maxwell-Poisson distribution (ZTCMP). The benefits of using the Conway-Maxwell-Poisson distribution (CMP) are that it includes the Bernoulli, Poisson and geometric distribution as special cases. It is also flexible for over- and under-dispersions relative to the original Poisson model. Moreover, the parameter estimates can be achieved by a simple linear regression approach. The uncertainty in estimating variances of the unknown population size under new estimator is studied with analytic and resampling approaches.The geometric distribution is one of the nested models under the Conway-Maxwell-Poisson distribution, the Turing and the Zelterman estimators are extended for the geometric distribution and its related model, respectively. Variance estimation and confidence intervals are constructed by the normal approximation method.An uncertainty of variance estimation of population size estimators for single marking capture-recapture data is studied in the final part of the research. Normal approximation and three resample approaches of variance estimation are compared for the Chapman and the Chao estimators. All of the approaches are assessed through simulations, and real data sets are provided as guidance for understanding the methodologies.