In this thesis, we study the empirical Bayesian estimation in normal and Poisson distributions using moment and maximum likelihood methods. To do this, we consider a conjugate normal-inverse-gamma prior for hyperparameters in case of normal model and obtain the empirical Bayesian estimators of the hyper parameters using the squared error loss function by moment and maximum likelihood methods. In case of Poisson model, we consider a gamma prior and calculate the Bayes posterior estimator of the parameter of the Poisson distribution and corresponding posterior expected loss under Stein loss faction. We also calculate the Bayes posterior estimator of the parameter under the squared error loss and the corresponding posterior expected loss. Moreover, we derive the empirical Bayes estimators of the parameter of the Poisson distribution with a conjugate gamma prior by two methods. Two applications are provided to illustrate the results.
