ENHANCED POPULATION SIZE ESTIMATION USING ZELTERMAN-TYPE ZERO-TRUNCATED DISCRETE LINDLEY DISTRIBUTION UNDER ONE-INFLATED POISSON COUNT DATA

Abstract

Capture-recapture analysis is widely used for population size estimation in various fields, including ecology, biology, social sciences and medicine. The Zelterman Poisson estimator obtained from Poisson distribution is commonly used for estimating population size in capture-recapture but it tends to underestimate counts when dealing with overdispersed data. To address this limitation, this paper proposes the Zelterman-type estimator (Zelterman-DLD) developed under Zero-Truncated Discrete Lindley (ZTDL) distribution for improved population size estimation. The paper evaluates the performance of two estimators; Zelterman-DLD and Zelterman Poisson estimator (Zelterman-POIS) using count data derived from a one-inflated Poisson distribution. These estimators were assessed across different population sizes under varying levels of one-inflation (10% and 20%). Variance estimation was performed using the conditioning technique, while relative bias (RBIAS) and relative root mean square error (RRMSE) were used to measure the performance of the estimators. Simulation results and application to real-life data shows that the Zelterman-DLD consistently outperforms the Zelterman-POIS, exhibiting lower RBIAS and RRMSE across all scenarios.

Keywords: Zelterman-DLD, Zelterman-POIS, One-inflated Poisson distribution, Variance estimation