Efficient Estimation Strategies for Estimating the Shape Parameter of the Birnbaum–Saunders Distribution Using Shrinkage Preliminary Test Type Estimators

In this paper, we are concerned with the point estimation of the shape parameter of the Birnbaum–Saunders (BS) distribution while fixing the scale parameter. Our goal is to improve the usual maximum likelihood estimator by incorporating both the sample information and the non-sample information which is available from the past. The suggested estimation strategies are based on the principles of linear shrinkage, preliminary test and a combination of both shrinkage and the preliminary test in an optimal way. The non-sample information is being tested using a preliminary test statistic by means of Wald’s procedure. The analytical expressions for the asymptotic bias and the asymptotic mean square error of the estimators under consideration have been derived. A comprehensive simulation study is also designed to investigate the performance of the estimators in small sample situations. The simulation results are in line with the derived mathematical results. A real-life data application has also been carried out to appraise the performance of the estimators.