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Advances in Decision Sciences
Volume 2014, Article ID 485629, 10 pages
http://dx.doi.org/10.1155/2014/485629
Research Article

Data Transformation for Confidence Interval Improvement: An Application to the Estimation of Stress-Strength Model Reliability

Department of Economics, Management and Quantitative Methods, Università degli Studi di Milano, Via Conservatorio, 7-20122 Milan, Italy

Received 31 July 2014; Revised 19 September 2014; Accepted 29 September 2014; Published 23 October 2014

Academic Editor: David Bulger

Copyright © 2014 Alessandro Barbiero. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.