Numerical Estimation Method for the Generalized Weibull Distribution Parameters

Abstract

In this study, a new estimation method using the Runge-Kutta iteration technique is presented to improve point estimation methods. The improved method has been applied to the generalized Weibull distribution, which is a member of a family of distributions (T-X family). The estimates of the generalized Weibull model parameters were derived using the Runge-Kutta and Bayesian estimation methods based on the generalized progressive hybrid censoring scheme, via a Monte Carlo simulation. The simulation results indicated that the Runge-Kutta estimation method is highly efficient and outperforms the Bayesian estimation method based on the informative and kernel priors. Finally, two real data sets were studied to ensure the Runge-Kutta estimation method can be used more effectively than the most popular estimation methods in fitting and analyzing real lifetime data.