Compare Bayes estimators under Different Priors with the Classical estimators for Maxwell-Boltzmann distribution
Abstract
In this study, different estimators were used for estimating scale parameter for the Maxwell–Boltzmann distribution, such as maximum likelihood estimator, moment estimator and the Bayes estimator, in three types when the prior distribution for the scale parameter is (SRIG) distribution and ,the non-informative prior distribution and, the natural conjugate family of priors when the Bayesian estimation based on Squared Loss Function. Several cases from Maxwell–Boltzmann distribution for data generating , for different sample sizes (small, medium, and large).The results were obtained by using simulation technique, Programs written using MATLAB-R2008a program were used. Simulation results shown that bayes estimation when the prior distribution is (SRIG) distribution with (a=b=3) gives the smallest value of MSE and MAE for all (n).And bayes estimation when the prior distribution is the non-informative prior distribution with ( c=6) gives the smallest value of MSE and MAE for all (n).
Keywords
The Maxwell–Boltzmann, Maximum likelihood method, Moment estimation method, Bayes method, the SRIG prior distribution, the non-informative prior distribution, the natural conjugate family of priors, mean squared errors, MSE, Mean Absolute Errors, MAE.Metrics