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A simulation study is carried put in order to compare the perfomance of the Lincoln Petersen and Chapman estimators for single capturerecapture or dual system estimation when the sizes of the samples or record systems are not fixed by researcher. Performance is explored through both bias and variability. Unless both record probabilities and population size are very small, the Chapman estimator performs better than the LincolnPetersen estimator. This is due to the lower varaibility of the Chapman estimator and because it is nearly unbiased for a set population size ande record probabilities wider than the set for which the LinconPetersen estimator is nearly unbiased. Thus, for those kin of studies where te record probabulity is high for at least one record system, such as census correction studies, it should be preferred the Chapman estimator
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