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December, 1959 Optimum Tolerance Regions and Power When Sampling From Some Non-Normal Universes
Irwin Guttman
Ann. Math. Statist. 30(4): 926-938 (December, 1959). DOI: 10.1214/aoms/1177706076


We assume familiarity with the concepts defined in [1] and [2], where optimum $\beta$-expectation tolerance regions and their power functions were found for $k$-variate normal distributions. The method used is to reduce this problem to that of solving an equivalent hypothesis testing problem. It is the purpose of this paper to find optimum $\beta$-expectation tolerance regions for the single and double exponential distributions, and to exhibit the corresponding power functions. Let $X = (X_1, \cdots, X_n)$ be a random sample point in $n$ dimensions, where each $X_i$ is an independent observation, distributed by some continuous probability distribution function. It is often desirable to estimate on the basis of such a sample point a region, say $S(X_1, \cdots, X_n)$, which contains a given fraction $\beta$ of the parent distribution. We usually seek to estimate the center 100 $\beta$% of the distribution and/or one of the 100 $\beta$% tails of the parent distribution.


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Irwin Guttman. "Optimum Tolerance Regions and Power When Sampling From Some Non-Normal Universes." Ann. Math. Statist. 30 (4) 926 - 938, December, 1959.


Published: December, 1959
First available in Project Euclid: 27 April 2007

zbMATH: 0089.15303
MathSciNet: MR109399
Digital Object Identifier: 10.1214/aoms/1177706076

Rights: Copyright © 1959 Institute of Mathematical Statistics

Vol.30 • No. 4 • December, 1959
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