基于似然比检验的双截尾威布尔分布区间估计

Parametric Interval Estimation for Doubly-Truncated Weibull Distribution Based on Likelihood Ratio Test

针对现有的双截尾威布尔分布模型估计过程中点估计无解析解和缺少参数区间估计方法的问题,提出基于极值求解思想和蒙特卡罗方法的参数点估计数值求解方法和基于似然比检验理论的双截尾威布尔分布模型的参数区间估计方法。在计算过程中,提出随机数取值区间多步细分的变区间迭代数值求解方法。结合某数控外圆磨床故障间隔时间数据使用双截尾威布尔分布进行分析,并与两参数和三参数威布尔分布分析结果进行对比。实例结果表明,建立的变区间迭代算法和基于似然比检验理论的区间估计方法正确可行,具有较好的估计效果。

Since no analytical solution was found in the process of parametric point estimation as well as solution for the parametric interval estimation for Doubly-Truncated WeibuU distribution, an extreme value solution method and Monte Carlo method based parametric point estimation solution method and likelihood ratio test theory based parametric interval estimation method for Doubly-Truncated Weibull distribution model are proposed. During calculation, the multi-step detailed interval conversion iterative numerical solution method for random data interval is put forward further. On the basis of CNC external cylindrical grinding failure data, Doubly-Truncated Weibull distribution is used for analysis and comparison with two-parameter and three-parameter Weibull distribution. According to results, the interval conversion iterative algorithm set and likelihood ratio test theory based parametric interval estimation method are correct and available as a result of good estimation effect.