Estimate the Survival and Hazard functions by using the Simulation Technique for Modified Weibull Extension Distribution

In this paper, we study the modified Weibull extension distribution by utilizing the Monte Carlo method in the simulation procedure to generate various sample sizes with various replicates of the sample size and using this simulation to compare two estimation methods, the maximum likelihood estimator method and the rank set sampling estimator method, to get the best estimate for the unknown parameters of the modified Weibull extension distribution. It is noted that mean square error values for the maximum likelihood estimator method are better than mean square error values for the rank set sampling estimator method, which means that the maximum likelihood estimator method is the best for estimating the parameters of the modified Weibull extension distribution. Accordingly, we obtain an initial value from the best estimation for starting the process of applying this study in our lives on real data about patients who suffer from acute lymphocytic leukemia disease, and estimate the Survival and hazard functions of this state of patients.