Digital Experiment for Estimating Three Parameters and Their Confidence Intervals of Weibull Distribution

Abstract

Weibull distribution plays a very important role in fatigue statistics, because structural fatigue life mostly conforms to Weibull distribution rather than Gaussian distribution. However, the biggest obstacle to the application of Weibull distribution is the complexity of Weibull distribution, especially the estimation of its three parameters is difficult, and it is even more difficult to determine the confidence interval of each parameter. In order to solve the first problem, many methods have been proposed, such as the graph method, the analytical method, and the Gao Zhentong method proposed by me recently using the characteristics of Python. So, the question arises which method is better? To this end, referring to the idea and methods of machine learning, the concept of digital experiment is introduced. The digital experiment is carried out to determine the three parameters and their confidence interval of Weibull distribution. Experiments show that the Gao Zhentong method is indeed a better method for estimating the three parameters of Weibull distribution. Further, the bootstrap method that can be used for a digital experiment is introduced, and it is used to determine the three parameters and their confidence intervals of Weibull distribution. The results show that the three parameters and their confidence intervals of Weibull distribution can basically be determined at the same time.