Nearly unbiased estimators for the three-parameter Weibull distribution with greater efficiency than the iterative...

Area of Science:

• Statistics
• Reliability Engineering
• Probability Theory

Background:

• Maximum Likelihood Estimation (MLE) is standard for Weibull distribution parameter estimation.
• MLE often yields biased estimates for the three-parameter Weibull distribution.
• Addressing this bias is crucial for accurate reliability analysis.

Purpose of the Study:

• To develop a method for calculating weights to eliminate bias in MLE for the three-parameter Weibull distribution.
• To evaluate the performance of the proposed weighted MLE (WMLE) method.
• To compare WMLE with the traditional iterative MLE.

Main Methods:

• Derivation of exact and expected weights for bias cancellation in MLE equations.
• Utilizing Monte Carlo simulations to assess the WMLE method's effectiveness.
• Comparison of bias and variability reduction between WMLE and iterative MLE.

Main Results:

• The proposed weighted MLE method effectively cancels biases in parameter estimation.
• Bias is reduced by a factor of 7 compared to iterative MLE, regardless of sample size.
• Variability reduction by a factor of 7 is observed for small sample sizes, diminishing with larger samples.

Conclusions:

• The weighted MLE method provides a practical and effective solution for biased parameter estimates in the three-parameter Weibull distribution.
• WMLE offers significant improvements in bias reduction and, for small samples, variability reduction.
• This method enhances the accuracy of Weibull distribution parameter estimation in various applications.