Improved nonparametric tolerance intervals based on interpolated and extrapolated order statistics

Derek S. Young, Thomas Mathew

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

The standard approach to construct nonparametric tolerance intervals is to use the appropriate order statistics, provided a minimum sample size requirement is met. However, it is well-known that this traditional approach is conservative with respect to the nominal level. One way to improve the coverage probabilities is to use interpolation. However, the extension to the case of two-sided tolerance intervals, as well as for the case when the minimum sample size requirement is not met, have not been studied. In this paper, an approach using linear interpolation is proposed for improving coverage probabilities for the two-sided setting. In the case when the minimum sample size requirement is not met, coverage probabilities are shown to improve by using linear extrapolation. A discussion about the effect on coverage probabilities and expected lengths when transforming the data is also presented. The applicability of this approach is demonstrated using three real data sets.

Original languageEnglish
Pages (from-to)415-432
Number of pages18
JournalJournal of Nonparametric Statistics
Volume26
Issue number3
DOIs
StatePublished - Jul 2014

Keywords

  • Box-Cox transformation
  • fractional order statistics
  • one-sided tolerance limit
  • tolerance package
  • two-sided tolerance interval

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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