In this study, a new estimation method using the Runge-Kutta iteration technique is presented to improve the maximum likelihood estimation method. 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, maximum likelihood, and Bayesian 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 maximum likelihood estimation and Bayesian estimation methods based on the informative and kernel priors. Finally, two real data sets were studied to ensure the Runge-Kutta estimation method can be used very effectively than the most popular estimation methods in fitting and analyzing real lifetime data.