三参数Weibull分布参数的极大似然估计数值解法

利用降阶思想,给出了一种新的求解三参数Weibull分布参数的极大似然估计数值方法。该方法首先假定形状参数已知,将三元方程组转化为二元方程组,并用二分法求解该二元方程组的数值解,然后将尺度参数和位置参数表示成形状参数的函数,此时极大似然函数仅是关于形状参数的单变量函数,再次应用二分法即可得出形状参数的最优估计结果。该算法稳定,不需要赋予初始值,对样本数量没有限制。与其他方法相比,具有计算精度高、运算速度快的优点,便于工程应用。

Advanced Algorithm for Maximum Likelihood Estimation of Three Parameter Weibull Distribution

According to the idea of order reducing,an advanced numerical algorithm is presented aimed at maximum likelihood estimation of three-parameter Weibull distribution.Firstly,the shape parameter is assumed to be known.And now,ternary likelihood equations can be turned into binary ones that are solved with the dichotomy.And then,scale and location parameters are the functions of shape parameter.Further,the maximum likelihood function is described as an unitary function of shape parameter.It is easy to be solved with the dichotomy.The new algorithm is stable and doesnot require input initial value,and thus it is immune from the limitation of the number of samples.Compared with other algorithms,it has the advantages of high accuracy and fast operation speed,thus it is convenient in engineering application.