Estimation for the Weibull Extension Model Parameters based on Runge-Kutta Method

Abstract

Abstract In parameter estimation techniques, the maximum likelihood estimation method is the most common technique that is broadly used in social science and psychology, despite the fact that it is usually biased when the sample sizes are small or the data are heavily censored. Thus, the main objective of this paper is to introduce a numerical iteration technique, which is the Runge-Kutta method for finding the parameter estimators. This method has been applied for deriving the estimators for the Weibull extension model parameters and compared with the maximum likelihood and Bayes methods via Monte Carlo simulations. The results are strongly favorable to the Runge-Kutta method, which provides better estimates and outperforms the Bayes and maximum likelihood methods. Finally, numerical examples are given to demonstrate the efficiency of the proposed methods.