The statistical inferences about the parameters of Binomial-Poisson hierarchy model are discussed. Based on the estimators of paired observations we consider the other two cases with extra observations on both the first and second layer of the model. The MLEs of lambda and p are derived and it is also proved the MLE lambda is also the UMVUE of lambda. By using multivariate central limit theory and large sample theory, both the estimators based on extra observations on the first and second layer are obtained respectively. The performances of the estimators are compared numerically based on extensive Monte Carlo simulation. Simulation studies indicate that the performance of the estimators is more efficient than those only based on paired observations. Inference about the confidence interval for p is presented for both cases. The efficiency of the estimators is compared with condition given that same number of extra observations is provided.
