Weibull形状参数加权极大似然估计的偏差修正

Bias correction for weighted maximum likelihood estimation of Weibull shape parameters

针对在小样本下加权最大似然方法(WMLE)估计形状参数存在偏差的问题,本文研究了在小样本情形下(样本量为3~15)加权极大似然估计形状参数(β>1)的偏差修正方法,提出了关于样本量的两个偏差修正函数,易于使用。通过蒙特卡洛(Monte Carlo)仿真,在不同的威布尔模型、不同小样本量下,验证了本文偏差修正方法估计的形状参数的准确性和有效性。最后通过实例分析,表明本文偏差修正方法具有可行性。

There is bias in estimating shape parameters(β>1)using the weighted maximum likelihood method(WMLE)under small samples.Hence,we study the bias correction method for weighted maximum likelihood estimation of shape parameters in the small sample case(sample sizes of 3 to 15),and two bias correction functions about the sample size are proposed,which are easy to use.By Monte Carlo simulation,the accuracy and validity of the shape parameters estimated by this bias correction method are verified under different Weibull models and different small sample sizes.The example shows that the bias correction method is feasible.