Comparison of Estimators of the Weibull Distribution

Abstract

We compare the small sample performance (in terms of bias and root mean squared error) of the L-moment estimator of a three-parameter Weibull distribution with maximum likelihood estimation (MLE), moment estimation (MoE), least-square estimation (LSE), the modified MLE (MMLE), the modified MoE (MMoE), and the maximum product of spacing (MPS). Overall, the LM method has a tendency to perform well as it is almost always close to the best method of estimation. The ML performance is remarkable even at a small sample size of when the shape parameter lies in the [1.5, 4] range. The MPS estimator dominates others when . For large , MMLE outweighs others in samples of size , whereas LM is preferred in samples of size .

• 62F10
• 62F86

• Weibull distribution
• Order statistics
• L-moment estimation
• Maximum likelihood estimation
• Methods of moments
• Maximum product of spacing

Acknowledgment

We thank the anonymous referees for their helpful, and constructive comments and suggestions on an earlier draft of the article. We are highly indebted to Jonathan R. M. Hosking (Statistical Analysis and Forecasting, IBM T. J. Watson Research Center, USA) for e-mail correspondence and his helpful insights on issues related with the L-moment estimation.