Improved confidence intervals for the exponential mean via tail functions. Issue 2 (17th January 2016)

• Record Type: Journal Article
• Authors: Puza, Borek; Yang, Mo
• Is Part Of: Communications in statistics. Volume 45:Issue 2(2016)
• Page Start: 529
• Page End: 539
• Publication Date: 2016-01-17
• Subjects: Confidence interval -- Exponential distribution -- Optimality -- Probability of false coverage -- Reliability -- Tail function; Primary: 62F25 -- Secondary: 62F99; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2013.833235
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: The method of tail functions is applied to confidence estimation of the exponential mean in the presence of prior information. It is shown how the "ordinary" confidence interval can be generalized using a class of tail functions and then engineered for optimality, in the sense of minimizing prior expected length over that class, whilst preserving frequentist coverage. It is also shown how to derive the globally optimal interval, and how to improve on this using tail functions when criteria other than length are taken into consideration. Probabilities of false coverage are reported for some of the intervals under study, and the theory is illustrated by application to confidence estimation of a reliability coefficient based on some survival data.