摘要
本文应用极小值分布的样本矩来间接估计两参数威布尔分布的分布参数,并证明了所得到的威布尔分布参数的矩估计是有偏的;在实验的基础上,从一个近似分布出发,推导出了威布尔分布参数矩估计的修偏系数计算公式,因此获得了威布尔分布参数的基于极小值样本矩的一致渐近的近似无偏矩估计。通过计算机模拟方法,把矩估计和其它几种常用估计(极大似然估计、最好线性无偏估计和最小二乘方估计)进行了比较,所得结果是令人满意的。
In order to make clear the contribution of this paper, it is necessary togive a concise commentary on previous research. There have appeared many estimators for estimating the parameters of theWeibull distribution [1-8]. Even so, only three of the many types of the esti-mators summarised in ref. [5] -the maximum likelihood estimators, thebest linear unbiased estimators, and the least squares estimators -are reallyemployed in engineering. The outstanding advantage of these estimators lies inthat they can be used to process complete or censored life data. However, theauthors are of the opinion that the mathematical operations of these estimatorsappear to be comparatively tedious when only complete life data need to beprocessed. The moment estimators in ref. [6] reduce the tediousness of themathematicel operations, but the estimation results are not very satisfactory,particularly the precision attained is not quite as good as is desirable. A typeof the moment estimators possessing the simplest computing formulas, based onlog-Weibull sample mean and variation, was presented in ref. [8], but ref. [5]points out that moment estimation of ref. [8] is the worst estimation of theWeibull parameters because of unsatisfactory biases and precision. The authorsbelieve further that it is impossible to derive rigorous bias-correction formulasto improve the estimation precision of ref. [8]. The authors believe that the contribution of this paper is that a set ofsimple approximate bias-correction formulas for the moment estimators in ref.[8] is presented. As a result, the authors obtain modified moment estimators,which retain the highly desirable simplicity of ref. [8], and which, though notrigorously unbiased, are consistent, asymptotic, and approximately unbiased. Theresults of simulation study appear to indicate that the precision of the proposedmoment estimators is not lower than that of any other type of estimators.
出处
《西北工业大学学报》
EI
CAS
CSCD
北大核心
1990年第1期61-69,共9页
Journal of Northwestern Polytechnical University
关键词
矩估计
威布尔分布
参数
moment estimators
Weibull distribution.
