A Simplified Formulation of Likelihood Ratio Confidence Intervals Using a Novel Property

This article describes a novel property of likelihood ratio (LR) confidence intervals which is subsequently used to formulate an alternative approach for their calculation. It is shown that LR confidence limits can be defined as the minimum and maximum values of a parameter (or a function of parameters) that satisfy a set value of the log-likelihood. The proposed formulation allows straightforward implementation in end-user computing settings and it is particularly useful for the computation of intervals on noninvertible functions of model parameters. The main goal of the article is to expose this little-known property of LR confidence limits to the practitioner and research communities. Two case studies based on applications in product quality and reliability improvement are used for illustration. The first case study deals with interval estimation of the difference between the means of two lognormal populations. The second application concerns interval estimation for misclassification probabilities attributable to measurement error. Supplementary materials for this article are available online.