威布尔分布三参数的拟合特性

利用Monte Carlo方法分别考察了由相关系数优化法、概率权重矩估计法和最大似然法拟合得到的威布尔分布三参数的分布规律和相关性，在指定置信度下给出了Monte Carlo模拟求得的三参数置信区间。以安全寿命的置信区间大小作为判据，对拟合参数的3种方法进行了比较。结果表明，3种方法拟合得到的参数和安全寿命近似服从正态分布，形状参数与尺度参数存在正相关，而位置参数与前两个参数存在负相关。拟合数据的最佳方案是先用相关系数法求参数初值，再用最大似然法进一步精确求解三参数。

Characteristics of Three Fitted Parameters for Weibull Distribution

The distribution and correlation of the fitted three parameters of Weibull distribution with the correlation coefficient method,probability weighted moment estimation method and maximum likelihood estimation method are reviewed by Monte Carlo simulation.Under the given confidence level,the confidence intervals of the three fitted parameters of Weibull distribution are presented based on the simulated results.The qualities of the above three fitting methods are valued under the same criterion of the confidence intervals of their safe fatigue lives.The results show that the distribution of the three fitted parameters of Weibull distribution meets the normal distribution,and the distribution of safe life likewise meets the normal distribution.The parameter of shape and the parameter of scale has a positive correlation,and the parameter of location is negative correlated to them.For practical purpose,it is suggested that the correlation coefficient method should be used first to get primaryvalues of the fitted parameters for the maximum likelihood method,then the more accurate fitted parameters will be got further.