WITHDRAWN: Interchangeability Among Confidence, Prediction, and Tolerance Intervals

• Author(s): Harry Yang
• Keywords: Confidence interval ; Predication interval ; Shelf life ; Tolerance interval

Abstract

Concepts of confidence, prediction and tolerance intervals are discussed. Assuming that the sampling distribution is normal, it is shown that the confidence interval (CI) and prediction interval (PI) are special cases of the tolerance interval (TI). Under such unified perspective, these interval approaches can be used and interpreted interchangeably. Two exact methods, one based on generalized confidence interval and the other exact integration, for determining tolerance bounds are developed. A simulation study is conducted to compare coverage probability of the methods to those currently in use. The unified view also makes it possible to evaluate different interval approaches in the same statistical context. An application of the unified method to drug shelf life estimation is provided.