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Tolerance intervals in statistical software and robustness under model misspecification
Journal of Statistical Distributions and Applications Pub Date : 2021-07-18 , DOI: 10.1186/s40488-021-00123-2
Kyung Serk Cho 1 , Hon Keung Tony Ng 2
Affiliation  

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.

中文翻译:

统计软件中的公差区间和模型错误指定下的稳健性

容差区间是一个统计区间,它以 100(1−α)% 的置信度覆盖至少 100ρ% 的感兴趣的总体,其中 ρ 和 α 是 (0, 1) 中预先指定的值。在许多科学领域,例如制药科学、制造过程、临床科学和环境科学,公差区间用于统计推断和质量控制。尽管容差区间很有用,但计算容差区间的过程通常不会在统计软件包中实现。本文旨在对一些常用统计软件包(包括 JMP、Minitab、NCSS、Python、R 和 SAS)中容差区间的计算程序进行比较研究。另一方面,我们还研究了错误指定潜在概率模型对容差区间性能的影响。我们通过蒙特卡罗模拟研究,在假设分布与真实基础分布相同以及假设分布与真实分布不同时研究容差区间的性能。我们还提出了一种稳健的模型选择方法,以获得对模型错误指定相对不敏感的公差区间。我们表明,当潜在分布未知但候选分布可用时,所提出的稳健模型选择方法表现良好。我们通过蒙特卡罗模拟研究,在假设分布与真实基础分布相同以及假设分布与真实分布不同时研究容差区间的性能。我们还提出了一种稳健的模型选择方法,以获得对模型错误指定相对不敏感的公差区间。我们表明,当潜在分布未知但候选分布可用时,所提出的稳健模型选择方法表现良好。我们通过蒙特卡罗模拟研究,在假设分布与真实基础分布相同以及假设分布与真实分布不同时研究容差区间的性能。我们还提出了一种稳健的模型选择方法,以获得对模型错误指定相对不敏感的公差区间。我们表明,当潜在分布未知但候选分布可用时,所提出的稳健模型选择方法表现良好。
更新日期:2021-07-19
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