Bayes Estimations for Parameter of the Poisson distribution with Progressive Schemes

This study introduces maximum likelihood and Bayesian approaches to Poisson parameter estimation using posterior distribution. I discuss three types of loss functions: the asymmetric linear exponential loss function, non-linear exponential loss function, and squared error loss function. Their performance is compared with the maximum likelihood estimator using mean squared error (MSE) as the test criterion. The proposed method with the classical estimator (maximum likelihood estimator) is better than that with the non-classical estimators for point estimation with different sample sizes. Maximum likelihood estimation provides the optimal performance in estimating the Poisson distribution, as evidenced by the asymptotically smallest MSE values. For small true parameter values the results reveal that the Bayesian approaches have good estimation performance.