Tolerance and Prediction Intervals for Non-normal Models

• URL: http://arxiv.org/abs/2011.11583v5
• Date: Mon, 17 Jan 2022 13:43:38 GMT
• Title: Tolerance and Prediction Intervals for Non-normal Models
• Authors: Geoffrey S Johnson
• Abstract summary: A prediction interval covers a future observation from a random process in repeated sampling. A tolerance interval covers a population percentile in repeated sampling and is often based on a pivotal quantity.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A prediction interval covers a future observation from a random process in repeated sampling, and is typically constructed by identifying a pivotal quantity that is also an ancillary statistic. Analogously, a tolerance interval covers a population percentile in repeated sampling and is often based on a pivotal quantity. One approach we consider in non-normal models leverages a link function resulting in a pivotal quantity that is approximately normally distributed. In settings where this normal approximation does not hold we consider a second approach for tolerance and prediction based on a confidence interval for the mean. These methods are intuitive, simple to implement, have proper operating characteristics, and are computationally efficient compared to Bayesian, re-sampling, and machine learning methods. This is demonstrated in the context of multi-site clinical trial recruitment with staggered site initiation, real-world time on treatment, and end-of-study success for a clinical endpoint.

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