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

机译：两参数Birnbaum-Saunders分布的鲁棒显式估计

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摘要

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.
机译：两参数Birnbaum-Saunders分布可广泛用于模拟疲劳材料的失效时间。它的最大似然估计器（MLE）对离群值非常敏感，也没有封闭形式的表达式。这激励我们开发一些替代估计量。在本文中，我们开发了两个鲁棒的估计器，它们也是样本观测值的显式函数，因此易于计算。我们推导了它们的故障点，并进行了广泛的蒙特卡洛模拟实验，以比较所考虑的所有估计器的性能。从仿真结果中可以看出，拟议的估计器的性能要优于MLE，但在实际情况下经常会出现数据污染的情况下，它们的性能要好得多。提出了一种简单的减少偏倚的技术来减少推荐估算器的偏倚。最后，以实际数据示例说明了所开发过程的实际应用。

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