![]() There are three types of statistical intervals commonly used in practice: confidence interval, prediction interval, and tolerance interval. We show that the proposed robust model selection approach performs well when the underlying distribution is unknown but candidate distributions are available. We also propose a robust model selection approach to obtain tolerance intervals that are relatively insensitive to the model misspecification. We study the performance of tolerance intervals when the assumed distribution is the same as the true underlying distribution and when the assumed distribution is different from the true distribution via a Monte Carlo simulation study. On the other hand, we also investigate the effect of misspecifying the underlying probability model on the performance of tolerance intervals. This paper aims to provide a comparative study of the computational procedures for tolerance intervals in some commonly used statistical software packages including JMP, Minitab, NCSS, Python, R, and SAS. Despite the usefulness of tolerance intervals, the procedures to compute tolerance intervals are not commonly implemented in statistical software packages. In many scientific fields, such as pharmaceutical sciences, manufacturing processes, clinical sciences, and environmental sciences, tolerance intervals are used for statistical inference and quality control. A tolerance interval is a statistical interval that covers at least 100 ρ % of the population of interest with a 100(1− α) % confidence, where ρ and α are pre-specified values in (0, 1). ![]()
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