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Abstract
In recent decades, it has been found that the three-parament Weibull distribution plays an increasingly important role in the fields such as structural fatigue and reliability. However, the complexity of estimating these three parameters greatly affects the application of the Weibull distribution. In the past three years, the author has successively proposed the Zhentong Gao Method and the Generalized Zhentong Gao Method, which have effectively solved this problem. However, it has also been found that there is room for improvement in these two methods. That's what this paper is about, how to use the characteristics of the Monte Carlo and Metropolis-Hastings methods to upgrade the Zhentong Gao method and the Generalized Zhentong Gao method, so that these two upgraded methods can not only efficiently estimate the three parameters of the Weibull distribution, but also provide their confidence intervals, and can be used in more fields.
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