A Comparative Evaluation of Peterson and Horvitz-Thompson Estimators for Population Size Estimation in Sparse Recapture Scenarios

Abstract

Estimating population size is essential in ecological and social studies, particularly when direct enumeration is infeasible. This study compares the Peterson and Horvitz-Thompson estimators using capture-recapture data from female drivers at Bahauddin Zakariya University (BZU) across seven sampling events. While both estimators produced similar point estimates ranging from 22 to 30 individuals, the Horvitz-Thompson estimator consistently exhibited lower variance and narrower confidence intervals, especially under sparse recapture conditions. For example, in event 6, both estimators returned a population estimate of 30; however, the Horvitz-Thompson variance (15.0) was significantly lower than Peterson's (35.0). These results underscore the robustness and statistical efficiency of inclusion-probability based estimators in real-world settings where uniform capture probabilities are unlikely.