Fitting the three-parameter Weibull distribution with Cross Entropy

The Weibull distribution is widely used in applications such as reliability and lifetime studies. Although this distribution has three parameters, for simplicity, literature pertaining to Weibull parameter estimation relaxes one of its parameters in order to estimate the other two. When the three-parameter Weibull distribution is of interest, the estimation procedure is complicated. For example, the likelihood function for a three-parameter Weibull distribution is hard to maximize. In this paper, a Cross Entropy (CE) method is developed in the context of maximum likelihood estimation (MLE) of a three-parameter Weibull distribution. Performing a simulation study, a comparative analysis between the newly developed method and two existing methods is conducted. The results show the proposed method has better performance in terms of accuracy, precision and run time for different parameter settings and sample sizes.