Comparison of methods to reduce the maximum likelihood bias on Weibull parameters

The maximum likelihood (ML) method is known to estimate the Weibull parameters with a certain bias. Recently two methods have been published to reduce the bias of the Weibull shape parameter. These methods concern: the use of a relative (or 'generalized') likelihood function; and an unbiasing formula. None of these two contributions studied the effect on the scale parameter. The present study compares both methods on the basis of Monte Carlo simulations. Some tests were applied to the random number sequences to select two representative series per sample size. For both methods the bias of the two Weibull pivotal functions were assessed together with their standard deviations.