A method of inference for a capture-recapture experiment in discrete time with variable capture probabilities

Abstract

The problem of heterogeneity of capture probabilities among the individuals of a population is a major outstanding problem in the estimation of population size. The ’jackknife‘ estimator developed by Burnham & Overton (1978) and the estimator of Chao (1989) are the available estimation procedures at present. Here, we provide alternative estimators for population size via martingale theory. A class of estimators is generated by a martingale estimating equation. Explicit expressions for the estimators and the associated standard errors are obtained which involve only simple computation. Two examples are given.

Keywords:

• beta distribution
• capture-recapture experiment
• jackknife estimator
• weight function
• zero mean martingales(ZMM)