Abstract–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.

中文翻译：

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使用新特性的似然比置信区间的简化公式

摘要——本文描述了似然比 (LR) 置信区间的一种新特性，该特性随后用于制定一种替代方法来计算它们。结果表明，LR 置信限可以定义为满足对数似然设定值的参数（或参数的函数）的最小值和最大值。所提出的公式允许在最终用户计算设置中直接实现，并且它对于计算模型参数的不可逆函数的区间特别有用。这篇文章的主要目标是向从业者和研究社区展示 LR 置信限制的这个鲜为人知的特性。使用基于产品质量和可靠性改进应用的两个案例研究进行说明。第一个案例研究涉及两个对数正态总体均值之间差异的区间估计。第二个应用涉及归因于测量误差的误分类概率的区间估计。本文的补充材料可在线获取。