Comparison of maximum likelihood unbiasing methods for the estimation of the Weibull parameters

The technique of unbiasing the maximum likelihood estimates of the scale and shape parameters of the Weibull function is discussed. The efficiency of recent and traditional unbiasing estimators is critically compared. In particular, the Bain-Engelhardt, Harter & Moore and Ross unbiasing methods are considered, together with the Jacquelin estimators. The behavior of these estimators and unbiasing factors is investigated as function of the sample size and the value of the shape parameter. It is shown that some procedures are actually not unbiasing at all but, depending on the value of the shape parameter and the sample size, can even make the ML estimates worse. The unbiasing factors proposed by Ross and Harter and Moore seem the most effective for the shape and scale parameters, respectively. When using the unbiasing factors on the point estimates, rather than on the expected values, it is found that these methods tend to lose their accuracy in some cases.