Numerical Estimation for the Three-Parameter Burr-XII Model Parameters Based on Picard’s Method

Abstract

Abstract In parameter estimation techniques, there are several methods for estimation in lifetime distributions and reliability theory. 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 estimation technique using Picard’s method for estimating the three-parameter Burr type-XII distribution parameters. A comparison between the Picard and Bayes methods is provided using an extensive Monte Carlo simulation based on two criteria, namely, the average bias and the mean squared error. The simulation results indicate that Picard’s method is highly efficient and outperforms the Bayes method based on the generalized progressive hybrid censoring scheme. Finally, two real dataset analyses are presented to illustrate the efficiency of the proposed methods.