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 of kis found by utilizing Equation (20). Then, through the estimated k value and Equation (19), the parameter σ is estimated and then the parameter c is obtained by adapting inverse transformation. Lastly, forb, using the estimated σ and k values and Equation (18), theparameter μ is obtained and then inverse transformation is conducted for the parameterb