Tolerance limits and tolerance intervals for ratios of normal random variables using a bootstrap calibration.
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.
Department of Mathematics and Statistics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD, 21250, USA.
Marilena
M
Flouri
Department of Mathematics and Statistics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD, 21250, USA.
Shuyan
S
Zhai
Department of Mathematics and Statistics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD, 21250, USA.
Thomas
T
Mathew
Department of Epidemiology and Biostatistics, Biostatistics Center, George Washington University, 6110 Executive Boulevard, Rockville, MD, 20852, USA.
Ionut
I
Bebu
D001699:Biometry / Q000379:methods*; D016001:Confidence Intervals; D003362:Cost-Benefit Analysis; D006801:Humans; D015233:Models, Statistical; D016011:Normal Distribution; D018709:Statistics, Nonparametric
Bootstrap calibration; Cost-effectiveness analysis; Lognormal distribution; Nonparametric tolerance limits; One-sided tolerance limit; Two-sided tolerance interval