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Tolerance intervals in statistical software and robustness under model misspecification

Author

Listed:
  • Kyung Serk Cho

    (Columbia University)

  • Hon Keung Tony Ng

    (Southern Methodist University)

Abstract

A tolerance interval is a statistical interval that covers at least 100ρ% of the population of interest with a 100(1−α)% confidence, where ρ and α are pre-specified values in (0, 1). 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. Despite the usefulness of tolerance intervals, the procedures to compute tolerance intervals are not commonly implemented in statistical software packages. 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. On the other hand, we also investigate the effect of misspecifying the underlying probability model on the performance of tolerance intervals. 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. We also propose a robust model selection approach to obtain tolerance intervals that are relatively insensitive to the model misspecification. We show that the proposed robust model selection approach performs well when the underlying distribution is unknown but candidate distributions are available.

Suggested Citation

  • Kyung Serk Cho & Hon Keung Tony Ng, 2021. "Tolerance intervals in statistical software and robustness under model misspecification," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-49, December.
    • Handle: RePEc:spr:jstada:v:8:y:2021:i:1:d:10.1186_s40488-021-00123-2
    DOI: 10.1186/s40488-021-00123-2
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    References listed on IDEAS

    as
    1. Derek S. Young & Thomas Mathew, 2014. "Improved nonparametric tolerance intervals based on interpolated and extrapolated order statistics," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(3), pages 415-432, September.
    2. Fernández, Arturo J., 2010. "Two-sided tolerance intervals in the exponential case: Corrigenda and generalizations," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 151-162, January.
    3. Young, Derek S., 2010. "tolerance: An R Package for Estimating Tolerance Intervals," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 36(i05).
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