威布尔分布参数估计方法的比较

Comparison of Parameter Estimation Methods of Weibull Distribution

给出了基于威布尔分布形状参数、尺度参数、位置参数的极大似然估计、L矩估计和矩估计的估计量,其中极大似然估计计算方法是新给出的计算方法。以偏差和均方误差为标准,综合比较这三种方法,运用Matlab程序得到了三个参数的偏差和均方误差变化的曲线图。通过对偏差和均方误差变化的曲线图分析比较,得到L矩估计方法性能最好,其次是极大似然估计,矩估计方法性能最差。

The maximum likelihood estimators of shape parameters,scale parameters,position parameters,L moment estimators and the estimators of moment estimators of Weibull distribution are given.The maximum likelihood estimation method is a new calculation method.The deviation and mean square error as the standard,the three methods comprehensively compared,MATLAB software is used to get the three parameters of the deviation and mean square error changes of the curve.By comparing the curves of deviation and mean square error,it is found that L-moment estimation method has the best performance,followed by maximum likelihood estimation,and moment estimation method has the worst performance.