In this study, utilizing the equations for the EGL1 distribution as given in Equations (18)–(20)and inverse transformation, the estimators of the parametersb,candkof the EBXII distributionare obtained and named as MMEs. To obtain the parameter estimates based on the MMEs, first,the estimate ofkis found by utilizing Equation (20). Then, through the estimatedkvalue andEquation (19), the parameterσis estimated and then the parametercis obtained by adaptinginverse transformation. Lastly, forb, using the estimatedσandkvalues and Equation (18), theparameterμis obtained and then inverse transformation is conducted for the parameterb