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Tolerance limits and tolerance intervals for ratios of normal random variables using a bootstrap calibration
Author(s) -
Flouri Marilena,
Zhai Shuyan,
Mathew Thomas,
Bebu Ionut
Publication year - 2017
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201600117
Subject(s) - tolerance interval , statistics , mathematics , nonparametric statistics , log normal distribution , confidence interval , normal distribution , bivariate analysis , sample size determination , parametric statistics , random variable , calibration , multivariate normal distribution , multivariate statistics
This paper addresses the problem of deriving one‐sided tolerance limits and two‐sided tolerance intervals for a ratio of two random variables that follow a bivariate normal distribution, or a lognormal/normal distribution. The methodology that is developed uses nonparametric tolerance limits based on a parametric bootstrap sample, coupled with a bootstrap calibration in order to improve accuracy. The methodology is also adopted for computing confidence limits for the median of the ratio random variable. Numerical results are reported to demonstrate the accuracy of the proposed approach. The methodology is illustrated using examples where ratio random variables are of interest: an example on the radioactivity count in reverse transcriptase assays and an example from the area of cost‐effectiveness analysis in health economics.