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A BETA‐BINOMIAL MODEL FOR ESTIMATING THE SIZE OF A HETEROGENEOUS POPULATION
Author(s) -
Yip Paul S.F.,
Xi Liqun,
Arnold Richard,
Hayakawa Yu
Publication year - 2005
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2005.00395.x
Subject(s) - jackknife resampling , mathematics , estimator , statistics , binomial (polynomial) , population size , sample size determination , population , econometrics , binomial distribution , beta distribution , demography , sociology
Summary This paper compares the properties of various estimators for a beta‐binomial model for estimating the size of a heterogeneous population. It is found that maximum likelihood and conditional maximum likelihood estimators perform well for a large population with a large capture proportion. The jackknife and the sample coverage estimators are biased for low capture probabilities. The performance of the martingale estimator is satisfactory, but it requires full capture histories. The Gibbs sampler and Metropolis‐Hastings algorithm provide reasonable posterior estimates for informative priors.