Numerical Inference on the Generalized Weibull Model Parameters Using Picard’s Method

Abstract In this study, numerical analysis has been used to introduce an optimal estimation method, Picard’s method, which outperforms the Bayes’ method. To clarify that, the point estimates for the generalized Weibull model parameters were derived using this method and compared with the Bayes’ method based on the informative gamma prior, kernel prior and characteristic prior, via Monte Carlo simulation based on the generalized progressive hybrid censoring scheme. The simulation results indicated that Picard’s method is highly efficient and outperforms the Bayes’ method. Finally, two real datasets were studied to ensure Picard’s method can be used more effectively than the most popular estimation methods in fitting and analyzing real-life data.