On the maximum likelihood estimation of parameters of Weibull distribution based on complete and censored data

The estimation of parameters of a Weibull distribution, requiring numerical methods, has been discussed by numerous authors. In this paper, an alternative approach based on a very simple and easy-to-apply graphical method is proposed, which also readily shows the existence and uniqueness of the maximum likelihood estimates. Furthermore, for censored data from a large sample size, a closed-form estimator for the shape parameter is also obtained.