伽马过程是分析单调退化数据的常用模型之一.对伽马退化模型进行参数估计需要假定其形状函数的具体形式. 然而,有时候可能并没有足够的信息来选择合适的函数形式,此时参数估计方法就不再适用. 针对Song 和 Cui (2022)所提出的二元伽马退化模型, 文章研究了其形状函数的非参数估计问题,提出了一种基于期望最大化算法的估计方法.文章通过数值模拟验证了所提方法的有效性,并进行了实例分析来说明该方法的应用.
Abstract
The gamma process is one of the widely used models for analyzing monotonic degradation data. Parametric estimation of the gamma process-based degradation models requires one to postulate specific forms for shape functions. However, there may sometimes be no enough information to determine appropriate functional forms, which makes the parametric estimation method inapplicable. Regarding the bivariate gamma degradation model proposed by Song and Cui (2022), this paper investigates the problem of estimating shape functions nonparametrically. An efficient estimation procedure is developed based on the expectation maximization algorithm. Numerical simulations are performed, and the results demonstrate the effectiveness of the proposed method. Finally, a real data set is analyzed for illustration.
关键词
期望最大化算法 /
伽马过程 /
非参数估计 /
可靠性 /
形状函数
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Key words
Expectation maximization algorithm /
Gamma process /
nonparametric estimation /
reliability /
shape function
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参考文献
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脚注
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基金
国家自然科学基金,(12301375)资助课题.
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