三参数威布尔分布参数估算方法对比研究

Comparative Study on Parameter Estimation of Three-Parameter Weibull Distribution

提出了一种改进的最大似然法用于估算三参数威布尔分布参数。从累积分布函数、样本量、数据敏感性三个方面对比分析了相关系数法、最大似然法和灰色模型法三种参数估算方法的优劣性。研究得出:相关系数法和改进后的最大似然法估算的参数精度比灰度模型法高,灰度模型法对数据更敏感、参数估算值波动大,建议在飞机和发动机可靠性研究中采用相关系数法或最大似然法估算三参数威布尔分布参数。将威布尔分布应用在某飞机法向极值的研究中,结果表明该飞机法向过载极值符合三参数威布尔分布。建立的方法对于飞机和发动机结构可靠性研究具有一定的参考价值。

In this paper, an improved maximum likelihood method of three-parameter Weibull distribution is established.Correlation coefficient method, maximum likelihood method and gray model method are compared from the three aspects of cu-mulative distribution function, sample capacity and sensitivity on data. The analysis results show that correlation coefficientmethod and the improved maximum likelihood method are better in calculation accuracy than the gray model method, and thegray model method is more sensitive on data and has greater fluctuation in parameter value than the other methods. It＇s sugges-ted that the correlation coefficient method or the maximum likelihood method should be used to estimate parameters of the three-parameter Weibull distribution than the gray model method. Analysis of normal overload extreme values is carried out, andthe results show that its normal overload extreme values are conformed to the three-parameter Weibull distribution. The estab-lished method could provide references for the structural reliability research of aircraft and aero-engine.