航空学报 > 1992, Vol. 13 Issue (3): 153-162

三参数威布尔分布的置信限

傅惠民, 高镇同, 徐人平   

  1. 北京航空航天大学固体力学所 北京 100083
  • 收稿日期:1991-04-30 修回日期:1991-07-15 出版日期:1992-03-25 发布日期:1992-03-25

CONFIDENCE LIMITS OF THREE-PARAMETER WEIBULL POPULATION PERCENTILES

Fu Hui-min, Gao Zhen-tong, Xu Ren-ping   

  1. Institute of Solid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing, 100083
  • Received:1991-04-30 Revised:1991-07-15 Online:1992-03-25 Published:1992-03-25

摘要:

本文给出了三参数威布尔分布置信限曲线的一般函数关系式,提出了一种利用秩分布确定该关系式中参数的方法,从而求得三参数威布尔分布的单侧置信限和双侧置信区间。该方法便于工程应用,并且可以推广到其他连续分布的情况。

关键词: 三参数威布尔分布, 单侧置信限, 置信区间

Abstract:

The confidence limits of Weibull population percentiles have become prominent in engineering design, but there is still no method by which those of three-parameter Weibull population percentiles are statisfactorily obtained. In this paper, a general function relation between the confidence limit of three-parameter Weibull population percentile and its percentage is given by means of Monte-Carlo simulation and fuzzy mathematics method. And a method of calculating the parameters in the relation is presented by the rank distribution. Using the method, one-sided confidence limits and two-sided confidence intervals of three-parameter Weibull population percentiles can be deter?imined at a given confidence level. This method is simple and convenient for application in engineering, and may also be applied to other continuous distributions. Many data of fatigue, durability, wind speed, instrument wavetube, earthquake and so on have been treated by the method with satisfaction.

Key words: three-parameter Weibull distribution, one-sided confidence limit, two-sided confidence interval