Estimating the Unknown Size of a Population based upon Re-parameterized Geometric Distribution
Keywords:
Capture-recapture data, heterogeneity, one-inflation, variance estimationAbstract
Estimating the unknown size of a partially observed population is challenging particularly when most of observed subjects are captured once. Geometric distribution, one of the most well-utilized discrete distributions in a capture-recapture setting, is re-parameterized corresponding to the uniform Poisson Ailamujia, a flexible model for data set with excesses of ones. The maximum likelihood and Generalized Turing estimators using uniform Poisson Ailamujia distribution were proposed. We address achieving variance estimates of population size estimators by using conditioning approach. In simulation studies, potential of the proposed estimators as well as the confidence interval are investigated and compared to conventional estimators developed on the basis of geometric distribution.
All estimators behaved similarly and the presented confidence intervals can improve the estimation.
As an application, two real data examples are examined using the proposed estimators.
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