Optimizing Robust Shape Parameter: Improved Methodologies for Birnbaum–Saunders Distribution

This study strives to improve the estimation of robust estimator when dealing with a univariate Birnbaum–Saunders distribution’s shape parameter while integrating both sample information and non-sample information keeping the scale parameter fix. The linear shrinkage robust estimator, preliminary test robust estimator, and shrinkage preliminary test robust estimator are recommended as the three types of point estimating methodologies for more effective estimation results. Additionally, the use of a Wald’s test statistic to investigate the non-sample data is advised. We examined the asymptotic theoretical properties of the suggested estimators using simulation studies. The performance of the estimators is evaluated based on simulated relative efficiency. Our simulation results provide strong evidence in favor of asymptotic theory. The effectiveness of the suggested estimation methodologies in actual data applications is demonstrated as well.