Numerical Inference on the Generalize Gamma Distribution Parameters Using Runge-Kutta Method

In statistical inference, there are several methods for estimating the distribution parameters in life data analysis. However, most of them are less efficient than the Bayes’ method based on the informative prior. Thus, the main objective of this study is to present an optimal numerical iteration method, such as the Runge-Kutta iteration technique, for estimating the distribution parameters. This method has been used for estimating the generalized life distribution parameters and comparing them with the Bayesian estimates based on the informative gamma and kernel priors. A comparison between these methods is provided by using an extensive Monte Carlo simulation study. The simulation results indicated that the Runge-Kutta method is highly favorable and outperforms the Bayesian estimates using different loss functions based on the generalized progressive hybrid censoring scheme. Finally, two real dataset analyses are presented to illustrate the efficiency of the proposed methods.