Journal
INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS
Volume 22, Issue 12, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219455422501255
Keywords
Three-parameter Weibull distribution; iterative method; location parameter; scale parameter; Monte Carlo simulation
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Funding
- National Science and Technology Major Project [J2019-V-0009-0103]
- China Postdoctoral Science Foundation [2021T140098]
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This paper investigates the parameter estimation issue of the three-parameter Weibull distribution in the context of small sample size. The results show that by empirically determining the shape parameter and using an iterative method for estimating the location parameter and scale parameter, the parameters of the three-parameter Weibull distribution can be more accurately estimated than using the maximum likelihood method.
The three-parameter Weibull distribution is popular in reliability analysis. However, in the context of a small sample size, the issue of parameter estimation of the three-parameter Weibull distribution is difficult to address. If only a small sample size is available, a reasonable method is to empirically determine the shape parameter, and the emphasis is placed on location parameter estimation. This paper presents a theoretical model to establish the relationship between the location parameter, the minimal sample value, and the sample size. Moreover, an iterative method is proposed to estimate the Weibull location parameter and scale parameter with an empirical value for the shape parameter. Compared with the maximum likelihood method (MLE), the Weibull plot with the sample correlation coefficient and TL-moment, the proposed method can more effectively estimate the parameters of the three-parameter Weibull distribution.
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