Improved Robust Estimation Techniques for the Scale Parameter of Birnbaum-Saunders Distribution

This study investigates the performance of improved estimation of robust estimators for the scale parameter of Birnbaum-Saunders distribution integrating sample information and unknown previous knowledge (non-sample information) by fixing the shape parameter. The three classes of point estimation techniques, linear shrinkage robust estimator, preliminary test robust estimator, and shrinkage preliminary test robust estimator are suggested for more efficient estimation. It is also recommended to use a Wald's test statistic to examine the non-sample data. The asymptotic theoretical properties of the recommended estimators are examined through simulation studies. The performance of the estimators is being evaluated based on simulated relative efficiency. Our simulation results decisively support asymptotic theory. A real data application is also carried out to demonstrate how effectively the suggested estimating methods work in practice.