Safari Muhammad Aslam Mohd, Masseran Nurulkamal, Majid Muhammad Hilmi Abdul, Tajuddin Razik Ridzuan Mohd
Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia.
Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia.
Sci Rep. 2025 Apr 3;15(1):11516. doi: 10.1038/s41598-025-96043-1.
Accurate estimation techniques are crucial in statistical modeling and reliability analysis, which have significant applications across various industries. The three-parameter Weibull distribution is a widely used tool in this context, but traditional estimation methods often struggle with outliers, resulting in unreliable parameter estimates. To address this issue, our study introduces a robust estimation technique for the three-parameter Weibull distribution, leveraging the probability integral transform and specifically employing the Weibull survival function for the transformation, with a focus on complete data. This method is designed to enhance robustness while maintaining computational simplicity, making it easy to implement. Through extensive simulation studies, we demonstrate the effectiveness and resilience of our proposed estimator in the presence of outliers. The findings indicate that this new technique significantly improves the accuracy of Weibull parameter estimates, thereby expanding the toolkit available to researchers and practitioners in reliability data analysis. Furthermore, we apply the proposed method to real-world reliability datasets, confirming its practical utility and effectiveness in overcoming the limitations of existing estimation methodologies in the presence of outliers.
精确的估计技术在统计建模和可靠性分析中至关重要，这些技术在各个行业都有重要应用。三参数威布尔分布是这方面广泛使用的工具，但传统估计方法常常难以处理异常值，导致参数估计不可靠。为解决这一问题，我们的研究引入了一种针对三参数威布尔分布的稳健估计技术，利用概率积分变换，特别是采用威布尔生存函数进行变换，重点关注完整数据。该方法旨在增强稳健性的同时保持计算简便，易于实现。通过广泛的模拟研究，我们证明了所提出的估计器在存在异常值情况下的有效性和弹性。研究结果表明，这种新技术显著提高了威布尔参数估计的准确性，从而扩展了可靠性数据分析中研究人员和从业者可用的工具集。此外，我们将所提出的方法应用于实际的可靠性数据集，证实了其在克服现有估计方法在存在异常值时的局限性方面的实际效用和有效性。
