Estimation of the Generalized Exponential Distribution Parameters Based on Picard’s Method

In statistical inference, Bayes’ method is the most commonly applicable in reliability analysis, despite its subjectivity to prior information other than data. Therefore, the main objective of this work is to introduce an efficient numerical method, Picard’s method, as a tool for estimation in statistical inference and compatible with Bayes’ method. The proposed method has been applied to the generalized exponential distribution parameters and compared to Bayes’ method based on different priors via Monte Carlo simulation. The simulation results indicated that Picard’s method provides better estimates and outperforms Bayes’ method based on the generalized progressive hybrid censoring scheme. Finally, two real datasets have been analyzed for illustrations and comparison of the proposed methods.