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In this article, we have primarily studied the Bayes’ estimator of the parameter of the Weighted Maxwell Boltzmann Distribution under the extended Jeffrey’s prior, Gamma & Chi-square 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 &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. The future research may be consider to estimate the parameters using different loss functions especially Linex loss function and Generalized entropy Loss function under different prior distributions like Conjugate priors and double priors etc.

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