Inference on the Weibull distribution based on record values

Record data are commonly seen in everyday life, e.g., concentration of emerging contaminants in environmental studies. Based on record data, this study investigates point estimation and confidence intervals estimation for the Weibull distribution. The uniformly minimum variance unbiased estimator for the Weibull shape is derived. Based on this estimator, a bias-corrected estimator for the Weibull scale is obtained and it is shown to have much smaller bias and mean squared error compared with the maximum likelihood estimator. Confidence intervals for parameters and reliability characteristics of interest are constructed using pivotal or generalized pivotal quantities. Then the results are extended to the stress–strength model involving two Weibull populations with different parameter values. Construction of confidence intervals for the stress–strength reliability is discussed under both equal shape and unequal shape scenarios. Extensive simulations are used to demonstrate the performance of confidence intervals constructed using generalized pivotal quantities.