Nearly unbiased estimators for the three-parameter Weibull distribution with greater efficiency than the iterative likelihood method

摘要

The maximum likelihood estimation (MLE) method is the most commonly used methodto estimate the parameters of the three-parameter Weibull distribution. However, itreturns biased estimates. In this paper, we show how to calculate weights which cancelthe biases contained in the MLE equations. The exact weights can be computed whenthe population parameters are known and the expected weights when they are not.Two of the three weights' expected values are dependent only on the sample size,whereas the third also depends on the population shape parameters. Monte Carlosimulations demonstrate the practicability of the weighted MLE method. Whencompared with the iterative MLE technique, the bias is reduced by a factor of 7(irrespective of the sample size) and the variability of the parameter estimates is alsoreduced by a factor of 7 for very small sample sizes, but this gain disappears for largesample sizes.