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In this paper, we have introduced weighted Maxwell-Boltzmann distribution and abbrivated as WMD. Different characteristic properties of the introduced distribution have been studied in detail. Although the estimators are not derived in a closed form but parametrs are estimated through the fitting of WMD to a particular data sets using the technique of MLE. In order to show the validilty, potentiality and flexibility of WMD in statistical modelling, we have fitted it to four different types of data sets. After the fitting of WMD to the considered data sets, comparison has been made between the special cases of WMD in terms of having least values of BIC, AIC & AICC. Random numbers from WMD are generated by using the Inverse Cdf method. Simulation has been carried out with the help of programming language R.

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