Approximate Distributional Results Based on the Maximum Likelihood Estimators for the Weibull Distribution

Simple approximations which are useful for constructing confidence intervals for the parameters, tolerance limits and confidence limits on reliability, based on maximum likelihood estimators, are studied in this paper. A new approximation for the distribution of the maximum likelihood estimator of the shape parameter is proposed, which works equally well for both complete and censored cases. Small-sample properties of some asymptotic results for the scale parameter, tolerance limits and reliability are also considered. The accuracy of these approximations is studied by comparing them to some existing Monte Carlo simulation results available in the literature.