Bias Reduction of Modified Maximum Likelihood Estimates for a Three-Parameter Weibull Distribution

In this work, we investigate the parameter estimation problem based on the three-parameter Weibull models, for which non-finite estimates may be obtained for the log-likelihood function in some regions of the parametric space. Based on an information criterion with penalization of the modified log-likelihood function, we propose a new class of estimators for this distribution model. In addition to providing finite estimates for the model parameters, this procedure reduces the bias of the modified estimator. The performance of the new estimator is evaluated through simulations and real-life data set modeling. An economic application on a real data set is discussed, as well as an engineering one.