Parameter Estimation of Weighted Maxwell-Boltzmann Distribution Using Simulated and Real Life Data Sets

Abstract

This paper deals with estimation of parameters of Weighted Maxwell-Boltzmann Distribution by using Classical and Bayesian Paradigm. Under Classical Approach, we have estimated the rate parameter using Maximum likelihood Estimator. In Bayesian Paradigm, we have primarily studied the Bayes’ estimator of the parameter of the Weighted Maxwell-Boltzmann Distribution under the extended Jeffrey’s prior, Gamma and exponential prior distributions assuming different loss functions. The extended Jeffrey’s prior gives the opportunity of covering wide spectrum of priors to get Bayes’ estimates of the parameter – particular cases of which are Jeffrey’s prior and Hartigan’s prior. A comparative study has been done between the MLE and the estimates of different loss functions (SELF and Al-Bayyati’s, Stein and Precautionary new loss function). From the results, we observe that in most cases, Bayesian Estimator under New Loss function (Al-Bayyati’s Loss function) has the smallest Mean Squared Error values for both prior’s i.e., Jeffrey’s and an extension of Jeffrey’s prior information. Moreover, when the sample size increases, the MSE decreases quite significantly. These estimators are then compared in terms of mean square error (MSE) which is computed by using the programming language R. Also, two types of real life data sets are considered for making the model comparison between special cases of Weighted Maxwell-Boltzmann Distribution in terms of fitting.