Maximum likelihood prediction of records from 3-parameter Weibull distribution and some approximations

Based on record data, numerous authors have discussed the estimation of two-parameter Weibull distribution using classical and Bayesian approaches. In this paper, prediction of future records based on observed ones, using the maximum likelihood method, is considered. For a restricted parametric space, the existence and uniqueness of the maximum likelihood predictors of future records as well as the predictive maximum likelihood estimators of all unknown quantities are also established. Alternative approximate methods to obtain the likelihood estimators and predictors, which always exist and are easy-to-determine, are also discussed. The alternative approximate procedures studied in this paper are transformation-based predictive likelihood function, corrected predictive likelihood function, maximum product of spacings prediction Monte Carlo simulations are performed to compare the proposed methods and one real data set is also analyzed for illustrative purposes.