Comparison of Estimators of the Weibull Distribution

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.

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