Ranked set sampling (RSS) has been proved to be an efficient sampling design for parametric and non-parametric inference. In this paper, we consider RSS-based estimation for the two-parameter Birnbaum–Saunders (BS) distribution, which is widely used in reliability analysis. The estimation methods considered for comparison purposes were: maximum likelihood (ML), modified method of moments (MMM), maximum product of spacings (MPS), and Anderson–Darling (AD). The performance of the RSS-based estimators was evaluated through Monte Carlo simulations under both perfect and imperfect ranking assumptions. The bias, mean squared error, and mean integrated squared error were used as the criteria for comparison. The results revealed that the RSS-based estimators perform better than their simple random sampling (SRS) counterparts. The ML estimator performed the best under the perfect ranking assumption, while the MMM provided better performance for higher levels of imperfect ranking. Additional simulations based on data from a forest inventory corroborated our findings.

中文翻译：

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基于二参数 Birnbaum-Saunders 分布的排序集抽样的估计

排序集抽样 (RSS) 已被证明是用于参数和非参数推理的有效抽样设计。在本文中，我们考虑了基于 RSS 的二参数 Birnbaum-Saunders (BS) 分布估计，该分布广泛用于可靠性分析。用于比较目的的估计方法是：最大似然法 (ML)、修正矩法 (MMM)、最大间距乘积 (MPS) 和 Anderson-Darling (AD)。在完美和不完美的排名假设下，通过蒙特卡罗模拟评估了基于 RSS 的估计器的性能。偏倚、均方误差和平均积分方误差用作比较标准。结果表明，基于 RSS 的估计器比简单随机抽样 (SRS) 估计器的性能更好。ML 估计器在完美排名假设下表现最好，而 MMM 为更高级别的不完美排名提供更好的性能。基于森林清单数据的其他模拟证实了我们的发现。