Abstract:

It has been well-known that the maximum likelihood estimation method is based on the large sample size and the estimator is biased. For Weibull distribution, the maximum likelihood estimators don’t have explicit expression; This weakness complicates the correctness on the biasness. A moment method that has explicit expression for estimators of Weibull distribution has been developed by Sirvanci and Yang. This method was developed from mathematical perspective, especially for right censored situation. This paper elaborates this moment method, and develops confidence interval for unknown parameter and reliability function. Proofs of some key formulas, which are missed in the state-of-art, are presented in this paper. Simulation results show this moment method is closer to true parameters than the classical maximum likelihood estimation.