Weibull inference using trimmed samples and prior information

Trimmed samples are commonly used in several branches of statistical methodology, especially when the presence of contaminated data is suspected. Assuming that certain proportions of the smallest and largest observations from a Weibull sample are unknown or have been eliminated, a Bayesian approach to point and interval estimation of the scale parameter, as well as hypothesis testing and prediction, is presented. In many cases, the use of substantial prior information can significantly increase the quality of the inferences and reduce the amount of testing required. Some Bayes estimators and predictors are derived in closed-forms. Highest posterior density estimators and credibility intervals can be computed using iterative methods. Bayes rules for testing one- and two-sided hypotheses are also provided. An illustrative numerical example is included.