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March, 1956 Tolerance Regions
D. A. S. Fraser, Irwin Guttman
Ann. Math. Statist. 27(1): 162-179 (March, 1956). DOI: 10.1214/aoms/1177728355


In this paper definitions are given for three types of tolerance regions. For distribution-free tolerance regions, an analytic condition is derived for the characteristic function of the region. Examples of the application of the condition are considered. For $\beta$-expectation tolerance regions, a criterion for a good tolerance region is introduced, and it is shown that the problem of finding such a tolerance region can be reduced to that of finding a good test for an equivalent hypothesis-testing problem. Best tolerance regions are obtained for a number of single variate and multivariate problems involving normal distributions.


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D. A. S. Fraser. Irwin Guttman. "Tolerance Regions." Ann. Math. Statist. 27 (1) 162 - 179, March, 1956.


Published: March, 1956
First available in Project Euclid: 28 April 2007

zbMATH: 0070.37201
MathSciNet: MR76257
Digital Object Identifier: 10.1214/aoms/1177728355

Rights: Copyright © 1956 Institute of Mathematical Statistics

Vol.27 • No. 1 • March, 1956
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