一种三参数Weibull分布极大似然估计的求解方法

A Solution Method for 3-Parameter Weibull Distribution of Maximum Likelihood Estimation

提出了一种求解极大似然估计的新算法.根据极大似然估计原理求出尺度参数的表达式,把该表达式代入对数似然函数,使对数似然函数中只包含位置参数和形状参数,把求解非线性方程组问题变成了求解满足约束条件的最优化问题,使问题得到了简化.该法具有计算精度高、运算速度快的优点,利用EXCEL的规划求解即可求解,便于工程应用.

There are many methods for 3-parame ter Weibull distribution of parameter estimation. Maximum likelihood estimation is a commonly estimation method. In this paper, proposed the maximum likelihood estimate one new algorithm. According to principle of maximum likelihood estimation, scale parameter derived expression, the expression into the log-likelihood function, so that the log-likelihood function that contains only the location parameter and shape parameter, solving the problem of nonlinear equations is transformed into constraints to meet the conditions for solving optimization problems,so that problem has been simplified. The method has high precision, high speed computing advantages, use of EXCEL＇ s Solver can be solved.