Improved confidence intervals for the scale parameter of Burr XII model based on record values

Abstract

In this paper some different sorts of confidence intervals are considered for the scale parameter of the Burr type XII distribution based on the upper record values. In this regard, the coverage probability is adopted as a measure of improvement when the endpoints are the same for all types of confidence intervals. Proposed confidence intervals are based on the preliminary test estimator, Thompson shrinkage estimator and Bayes estimator with conjugate prior information. It is nicely demonstrated that the confidence intervals based on the above methodologies are superior to the equal tail confidence interval on specific intervals. Subsequently, to construct a uniformly dominant confidence interval, the result of Kubokawa (Ann Stat 22(1):290---299, 1994) is extended for dependent observations by making use of the information that exists in a covariate record value.