Posterior Analysis for the Maxwell Model : Theory, Method and Computation

The Bayesian approach to analyze different statistical models has developed great interest among analysts. Posterior distribution is the workbench of the Bayesian statisticians. It is obtained when prior information is combined with likelihood. Therefore the prior information is necessary for the Bayesian approach. The prior information is purely subjective assessment of an expert before any data have been observed. So here we consider different informative and non-informative priors and compare them to see which one is more suitable for our proposed model. The effort of current study is to explore the heterogeneous population using the Bayesian analysis for simple and mixture of the Maxwell distribution when data is censored and uncensored. Various types of comparisons of prior distributions for the parameter of the Maxwell distribution and loss functions are illustrated. We also consider Type I mixture of the Maxwell distribution which is member of the subclass of the exponential family. As an extension to this work, a comparisons of different loss functions are made. Moreover we have derived the limiting expressions for the Bayes estimators with their variances.