Robust explicit estimation of the two-parameter Birnbaum–Saunders distribution

Abstract

The two-parameter Birnbaum–Saunders distribution is widely applicable to model failure times of fatiguing materials. Its maximum-likelihood estimators (MLEs) are very sensitive to outliers and also have no closed-form expressions. This motivates us to develop some alternative estimators. In this paper, we develop two robust estimators, which are also explicit functions of sample observations and are thus easy to compute. We derive their breakdown points and carry out extensive Monte Carlo simulation experiments to compare the performance of all the estimators under consideration. It has been observed from the simulation results that the proposed estimators outperform in a manner that is approximately comparable with the MLEs, whereas they are far superior in the presence of data contamination that often occurs in practical situations. A simple bias-reduction technique is presented to reduce the bias of the recommended estimators. Finally, the practical application of the developed procedures is illustrated with a real-data example.

Keywords:

• Birnbaum–Saunders distribution
• sinh-normal distribution
• robustness
• outliers
• percentiles

2000 MSC:

• 62F10
• 62F35

Acknowledgements

The authors wish to thank anonymous reviewers for the valuable comments on the IF and the suggestion of references, which led to the improvement of the original manuscript.