Estimation Problem on a Tagging Experiment Including Incomplete Reports.

The estimation of population size by a tagging experiment including incomplete reports of the number of recaptured tagged fishes is considered. It is assumed that the sample is classified into two classes. In class 1 the reporting rate of recaptured tagged fish is 1, and in class 2 the rate may be less than 1. In this case the Petersen estimator and the Chapman type estimator based on the observation in class 1 (CTE) have been proposed, although large sample in class 1 is not expected. In this paper, we examine the effects of the observation in class 2 as additional information for the estimation of population size. Some estimators which include the observations in both classes, such as the modified maximum likelihood estimator (MMLE), are evaluated in senses of the bias and the mean squared error. As a result, if the sample size in class 1 is small and true reporting rate is high, then the MMLE is preferable to the CTE. In the other case, however, the CTE is superior to the estimators based on the observations in both classes.