威布尔分布极大似然估计的近似解析法  

Approximate Analytical Method of Maximum Likelihood Estimation of Weibull Distribution

作　　者：田叶 何和平 张愉 TIAN Ye;HE He-ping;ZHANG Yu(College of Economics and Management,China Jiliang University,Hangzhou 310018,China)

机构地区：[1]中国计量大学经济与管理学院,浙江杭州310018

出　　处：《数学的实践与认识》2023年第8期180-190,共11页Mathematics in Practice and Theory

摘　　要：生存分析和可靠性分析极其广泛地应用威布尔(Weibull)分布,而此分布中的形状参数和尺度参数通常用极大似然法以及相关数值方法来估计.分别基于摄动法和同伦分析法,在统计学文献中首次简便地找到了Weibull分布的参数极大似然估计的近似解析表达式,从而对繁琐且不太可靠的数值方法提供了一个重要补充.蒙特卡洛模拟表明,由这两种近似解析法得到的结果比利用牛顿法和optim函数得到的结果更加准确,从而说明本文所提出的近似解析方法具有相当高的可行性和准确性.利用与本文类似的方法,我们也可求得很多其它统计问题中的极大似然估计的近似解析表达式.Weibull distribution is commonly applied in survival analysis and reliability analysis,whose shape and scale parameters are most commonly estimated by maximum likelihood method and its related numerical methods.Based on the perturbation method and homotopy analysis method respectively,for the first time among the statistics literature,this paper conveniently obtains approximate analytical formulas of maximum likelihood estimates of the parameters in Weibull distributions,which are important complements to those tedious and unreliable numerical methods.Monte-Carlo simulations show that the results obtained by these two approximate analytical methods are more accurate than those obtained by Newton method and Optim function,which shows that the approximate analytical methods proposed in this paper are fairly feasible and accurate.Using the similar methods,we can also obtain the approximate analytical formulas of maximum likelihood estimates in many other statistical problems.

关 键 词：近似解析法 摄动法 同伦分析法 极大似然估计 

分 类 号：O212.1[理学—概率论与数理统计]