Estimation Of The Parameters And Some Functionals Of The Weibull Distribution From Generalized Censored Sample

Some parameters and functionals estimation problem of the two parametered Weibull distribution are considered based on the generalized censored sample. Firstly, the MLE of the shape and scale parameters are derived using the genetic algorithm .Secondly, the approximate Bayes estimator of the parameters, the hazard function and the survival function are given based on the MLE of the parameters. Thirdly, based on the complete sample and type II censored sample, two asymptotically optimal empirical Bayes estimators of the scale parameter are constructed by a newly defined kernel estimator when the shape parameter is known. Fourthly, a square consistent nonparametric estimator of the survival function is constructed based on the complete sample. Finally, some numerical simulation results are listed. The results show that all of methods given above are feasible and some of them are better than the usual methods ,thus can be used in the practical experiments.