Data Transformation for Confidence Interval Improvement: An Application to the Estimation of Stress-Strength Model Reliability. (22nd October 2014)

• Record Type: Journal Article
• Authors: Barbiero, Alessandro
• Other Names: Bulger David Academic Editor.
• Is Part Of: Advances in decision sciences. Volume 2014(2014)
• Publication Date: 2014-10-22
• Subjects: Decision making -- Periodicals; Decision making; Electronic journals; Periodicals; 519
• DOI: 10.1155/2014/485629
• Languages: English
• ISSNs: 2090-3359

Abstract

Abstract : In many statistical applications, it is often necessary to obtain an interval estimate for an unknown proportion or probability or, more generally, for a parameter whose natural space is the unit interval. The customary approximate two-sided confidence interval for such a parameter, based on some version of the central limit theorem, is known to be unsatisfactory when its true value is close to zero or one or when the sample size is small. A possible way to tackle this issue is the transformation of the data through a proper function that is able to make the approximation to the normal distribution less coarse. In this paper, we study the application of several of these transformations to the context of the estimation of the reliability parameter for stress-strength models, with a special focus on Poisson distribution. From this work, some practical hints emerge on which transformation may more efficiently improve standard confidence intervals in which scenarios.