基于MLE-SA的威布尔分布的参数估计

摘要

针对三参数威布尔分布模型复杂,采用精确解法直接进行参数估计求解的不足,提出基于极大似然估计(MLE)和模拟退火算法(SA)进行参数估计.该方法首先利用二分法等将似然函数的超越方程组转化为一元函数,并采用引入历史最优值的SA算法进行函数最大值的求解,避免了位置参数陷入局部最优解.以仿真和实际例证为基础,详细说明了该方法的优点和缺陷.结果表明:基于MLE-SA算法的联合估计在一定程度上能够对三参数威布尔分布的参数进行精确搜索,具有实际工程应用价值.%Aiming at the complexity of the three-parameter Weibull distribution model and the deficiency of the using of the exact solution to solve the parameter estimation directly,the parameter estimation based on the maximum likelihood estimation (MLE) and the simulated annealing algorithm (SA) is proposed in this paper.Firstly,the method of transcendental equations of likelihood function is transformed into an unary function by means of dichotomy.The SA algorithm which introduces historical optimal value is used to solve the maximum value of the function,which avoids the positional parameters falling into the local optimal solution.Based on the simulation and actual examples,the advantages and disadvantages of the method are described in detail.