Effect Analysis of Probability Estimators on Parameter Estimation of the Three-Parameter Weibull Distribution

The three-parameter Weibull distribution is one of the most widely used probabilistic models for the characterization of fatigue failure data. The linear regression estimation (LRE), the minimum discrepancy estimation (MDE), errors-in-variables estimation (EIV) as well as the least squares estimation (LSE) are generally applied in the estimation of Weibull parameters for their simplicity, in which probability estimators play an important role. In this paper, compared with five commonly used estimators, an optimal probability estimator with the four methods for different sample sizes is obtained by Monte Carlo simulations. The optimal probability estimator shows more robustness and higher accuracy. In conclusion, an optimal probability estimator of the midpoint rank is recommended for LRE, MDE and EIV especially with small samples in practical applications.