Modelling Population Size Using Horvitz-Thompson Approach Based on the Zero-Truncated Poisson Lindley Distribution

Capture-recapture analysis is applied to estimate population size in ecology, biology, social science, medicine, linguistics and software engineering. The Poisson distribution is one of the simplest models for count data and appropriate for homogeneous populations. On the other hand, it is found to underestimate the counts for overdispersed data. In this study, population size estimation using the mixture of Poisson and Lindley distribution is proposed. It can exhibit overdispersed, equidispersed and underdispersed data. Additionally, it is able to present count data with long tail. As a result of the problem of unobserved individuals, the zero-truncated Poisson Lindley distribution is considered. The parameter of distribution can be estimated using the maximum likelihood estimation. The Horvitz-Thompson estimator based on the zero-truncated Poisson Lindley distribution for modelling the population size is investigated in this study. Point and interval estimation of the target population are presented. The technique of conditioning is used for variance estimation of the population size. Relative bias, relative variance and relative mean square error are used for measuring the accuracy of the estimator. The simulation results show that the Horvitz-Thompson estimator under the zero-truncated Poisson Lindley distribution provides a good fit when compared to the zero-truncated Poisson distribution.