Journal of Statistical Theory and Practice

, Volume 8, Issue 2, pp 238–259 | Cite as

Comparison of Estimators of the Weibull Distribution

  • Muhammad Akram
  • Aziz HayatEmail author


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 n = 10 when the shape parameter β lies in the [1.5, 4] range. The MPS estimator dominates others when 0.5 ≤ β < 1.5. For large β ≥ 6, MMLE outweighs others in samples of size n ≥ 50, whereas LM is preferred in samples of size n ≤ 20.


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

AMS Subject Classification

62F10 62F86 


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Copyright information

© Grace Scientific Publishing 2014

Authors and Affiliations

  1. 1.Department of Epidemiology and Preventive MedicineMonash UniversityMelbourneAustralia
  2. 2.School of Accounting, Economics, 2nd FinanceDeakin UniversityMelbourneAustralia

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