Advancements in shrinkage estimation utilizing robust parameters for the Birnbaum-Saunders distribution in the case of multiple samples

Abstract

In this study, we expanded the improved estimation strategies for robust estimators of the Birnbaum-Saunders distribution for the shape parameter for multiple samples while integrating sample and uncertain prior information. We have used the following estimators: the Graybill-Deal type estimator, the linear shrinkage estimator, the pretest estimator, the shrinkage preliminary estimator, the James-stein and positive James-stein estimation techniques. We developed a test statistic to accept or reject the null hypothesis when considering uncertain prior information. We also explored the asymptotic properties of the proposed estimators. To evaluate their effectiveness, we conducted Monte Carlo simulations using various parameter values and sample sizes that align with our theoretical findings. Additionally, we included a real data example to illustrate the estimators performance in real life application.

Journal of Statistical Research 2025, Vol. 59, No. 1, pp. 65-79