(A) comparative study of parameter estimation in bernoulli trials with dependence

Abstract

This thesis is concerned with the comparison between four competing estimators in Bernoulli trials with dependence; Klotz, Price, Crow and Miles, and Kim and Bai. Bias and mean squared error of each estimator are compared by simulation technique. The simulation results show that the approximate maximum likelihood estimator suggested by Klotz and the ratio estimator by Price have the negative biases, which are serious for the case where p is small and $\lambda$ is large. Crow and Miles`` estimator has smaller bias than Klotz``s or Price``s. However, it requires a lot of computations to obtain the estimator. The estimator suggested by Kim and Bai is not only easy to calculate but also has considerably smaller bias than the other three estimators. The results also show that there exists no significant difference in the mean squared error of the four competing estimators.