A method for computing tolerance intervals for a location-scale family of distributions

Ngan Hoang-Nguyen-Thuy and K. Krishnamoorthy ()
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Ngan Hoang-Nguyen-Thuy: University of Louisiana at Lafayette
K. Krishnamoorthy: University of Louisiana at Lafayette

Computational Statistics, 2021, vol. 36, issue 2, No 12, 1065-1092

Abstract: Abstract The problems of computing two-sided tolerance intervals (TIs) and equal-tailed TIs for a location-scale family of distributions are considered. The TIs are constructed using one-sided tolerance limits with the Bonferroni adjustments and then adjusting the confidence levels so that the coverage probabilities of the TIs are equal to the specified nominal confidence level. The methods are simple, exact and can be used to find TIs for all location-scale families of distributions including log-location-scale families. The computational methods are illustrated for the normal, Weibull, two-parameter Rayleigh and two-parameter exponential distributions. The computational method is applicable to find TIs based on a type II censored sample. Factors for computing two-sided TIs and equal-tailed TIs are tabulated and R functions to find tolerance factors are provided in a supplementary file. The methods are illustrated using a few practical examples.

Keywords: Asymmetric location-scale; Bisection method; Bonferroni; Content; Coverage level; Equivariant estimators; type II censored (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00180-020-01031-w

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