根据威布尔分布的极大似然估计法(MLE),应用Newton-Raphson方法迭代求解,在VBA(Visual Basic for Application)环境下编制了自动化求解及绘图程序,对原始数据进行运算,运算结果与文献算例一致。但同时,Newton-Raphson迭代公式对于原始数据数量级较大和形状参数很大的情况,计算机程序会发生溢出的问题。因此,提出了归一化数据的极大似然估计法迭代公式,有效地解决了程序溢出问题。设计的VBA程序具有通用性,可以广泛地用于轴承润滑、汽车等速万向节的可靠性数据分析。
教育是推动社会发展进步的基石,具有塑造未来、引领发展的重要作用。数理统计主要研究统计量和概率分布,是统计学类专业的一门基础必修课程。它为农业、医疗和通信等领域提供了坚实的理论基础,其教学改革研究具有重要意义。产出导向教育(Outcomes-Based Education, OBE)理念鼓励学生在实践中学习,符合新时代对教育的期待。本文以数理统计中较为重要的最大似然估计为例,遵循OBE理念,通过问题驱动的方式进行教学设计,旨在培养学生的良好品德和实际应用能力。Education serves as the cornerstone for promoting social development and progress, playing a vital role in shaping the future and leading development. Mathematical statistics, which focuses on statistical measures and probability distributions, is a fundamental required course in the field of statistics. It provides a solid theoretical foundation for industries such as agriculture, healthcare, and communications, making research on its teaching reform of great significance. The Outcomes-Based Education (OBE) concept encourages students to learn through practice, aligning with contemporary expectations for education. Taking maximum likelihood estimation, a relatively important concept in mathematical statistics, as an example, this paper designs teaching based on the OBE concept through a problem-driven approach, aiming to cultivate students' good character and practical application abilities.
