Comparative studies between the Bayesian estimation and the maximum likelihood estimation of the parameter of the uniform distribution

The point estimation of the parameter theta of the uniform distribution U(0, theta) is discussed. The general form of the Bayesian estimation of theta is investigated under the weighted square loss function in the framework of Bayesian statistics, and the precise form of the Bayesian estimation of theta is obtained based on the given Pareto conjugate prior distribution. The comparisons between the Bayesian estimation that obtained in the framework of Bayesian statistics and the maximum likelihood estimation that obtained in the framework of classical statistics are studied from theory and simulation respectively. Results show that the Bayesian estimation of theta under the weighted square loss function is smaller than the maximum likelihood estimation of theta in the framework of classical statistic in numerical value, and the Bayesian estimation that obtained is the maximum likelihood estimations of the corresponding functions of theta, respectively.