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

The maximum likelihood estimation (MLE) method is the most commonly used method to estimate the parameters of the three-parameter Weibull distribution. However, it returns biased estimates. In this paper, we show how to calculate weights which cancel the biases contained in the MLE equations. The exact weights can be computed when the 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 Carlo simulations demonstrate the practicability of the weighted MLE method. When compared 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 also reduced by a factor of 7 for very small sample sizes, but this gain disappears for large sample sizes.