广义BS-极小值疲劳寿命分布的统计分析方法研究

Statistical Analysis Method Study of Generalized BS-Minimum Fatigue Life Distribution

论文提出一种新的疲劳寿命分布—两参数广义Birnbaum-Saunders极小值分布(BSMin(α,β)),研究了该分布的密度函数与失效率函数的图像特征。其次,给出了该分布在全样本下两个参数的分位数估计与回归估计,并通过蒙特卡罗模拟比较发现分位数估计较优,同时也探讨了两个参数的矩估计、极大似然估计以及对数矩估计。此外,论文还指出BSMin(α,β)分布取对数后用泰勒展开可近似看作两参数极小值分布,由此得到两个参数的近似区间估计,并通过蒙特卡罗模拟考察了近似区间估计的精度。最后,利用模拟数据说明了论文所提的点估计和近似区间估计方法的应用。

A new fatigue life distribution is proposed in this paper,called two-parameter generalized Birnbaum-Saunders Minimum fatigue life distribution BSMin(α,β).The image features of density function and failure rate function are studied for this distribution.Then the quantile estimations and regression estimations of two parameters are given for this distribution under full sample,and it can be concluded that quantile estimations are better through Monte-Carlo simulations.Besides,the moment estimations,maximum likelihood estimations and logarithmic moment estimations of two parameters are also discussed.Furthermore,the distribution BSMin(α,β)can be approximately regarded as twoparameter minimum distribution after the logarithm and Taylor expansion,therefore the approximate interval estimations of two parameters are obtained.The precisions of approximate interval estimations are investigated by Monte-Carlo simulations.Finally,the simulation data is used to illustrate the application of point estimation and approximate interval estimation methods.