东北大学学报（自然科学版）

东北大学学报（自然科学版） ›› 2025, Vol. 46 ›› Issue (7): 108-112.DOI: 10.12068/j.issn.1005-3026.2025.20240194

• 智能制造 • 上一篇    

基于统计最小差异原理的Weibull分布参数估计方法

谢里阳1(), 朱文慧2, 吴宁祥1, 杨小玉1   

  1. 1.东北大学 机械工程与自动化学院，辽宁 沈阳 110819
    2.中国国际工程咨询有限公司 国防业务部，北京 100048
  • 收稿日期:2024-10-26 出版日期:2025-07-15 发布日期:2025-09-24
  • 通讯作者: 谢里阳
  • 基金资助:
    国家科技重大专项(J2019-IV-0002-0069);国家科技重大专项(J2019-V-0009-0103)

Weibull Distribution Parameter Estimation Method Based on Statistical Minimum Diversity Principle

Li-yang XIE1(), Wen-hui ZHU2, Ning-xiang WU1, Xiao-yu YANG1   

  1. 1.School of Mechanical Engineering & Automation，Northeastern University，Shenyang 110819，China
    2.Defense Business Department，China International Engineering Consulting Corporation，Beijing 100048，China.
  • Received:2024-10-26 Online:2025-07-15 Published:2025-09-24
  • Contact: Li-yang XIE

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摘要：

针对Weibull分布的参数估计，构造1个尺度参数的伪估计量，可以通过寻找有关变量的极值点的方法得到参数估计值.该参数估计方法原理是，正确的位置参数和形状参数使得根据各样本值估计出的尺度参数之间的差异最小.本质上，参数估计是基于1组具有不确定性的数据（随机变量样本）反映出的特定规律来提取（总体）信息.然而，这种规律是统计意义上的规律，而不是确定意义上的规律.其在有关函数极值点出现位置方面的表现是，估计量的准确值并非一定出现在确定性意义上的极值点.研究表明，对于上述Weibull分布参数估计问题，准确分布参数所在点与理论上的极值点之间通常存在一定的偏离，在最小值判据中引入1个偏移值（将“一阶导数等于零”修改为“一阶导数等于1个大于零的值”），能够显著提高参数估计的精度和稳健性.大量参数估计案例表明，将偏移值取为0.1，使得根据不同样本得到的真实值为1 000的Weibull分布位置参数估计值的范围从0~1 500大幅度缩小为500~1 550.

关键词: Weibull分布, 位置参数, 参数估计, 极值判据, 稳健性

Abstract:

For the Weibull distribution parameter estimation， a pseudo-estimator of scale parameters is constructed， and the estimated parameter values can be obtained by finding the extreme point of relevant variables based on the principle that the right location parameter and shape parameter minimize the diversity of the scale parameter estimates associated with individual sample values. Essentially， parameter estimation extracts（overall）information based on specific patterns reflected by a set of data with uncertainty （random variable samples）. However， the pattern is statistical in nature rather than deterministic. In terms of the occurrence of extreme points in the related functions， the exact value of the estimater does not necessarily occur at the extreme point in a deterministic extreme point. It is shown that there is typically a deviation between the point where the exact parameter is located and the theoretical extreme point， and the accuracy and robustness of the parameter estimation method can be greatly improved by introducing an offset value in the minimum value criterion （modifying “the first derivative being equal to zero” to “the first derivative being equal to a value greater than zero”）. A large number of parameter estimation cases show that the range of the estimated value of the Weibull location parameter （true value is 1 000） is narrowed from 0~1 500 to 500~1 550 by taking an offset value of 0.1.

Key words: Weibull distribution, location parameter, parameter estimation, extreme value criterion, robustness

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