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June, 1949 A Graphical Determination of Sample Size for Wilks' Tolerance Limits
Z. W. Birnbaum, H. S. Zuckerman
Ann. Math. Statist. 20(2): 313-316 (June, 1949). DOI: 10.1214/aoms/1177730044


To determine the smallest sample size for which the minimum and the maximum of a sample are the $100 \beta %$ distribution-free tolerance limits at the probability level $\epsilon$, one has to solve the equation $N\beta^{N-1} - (N - 1)\beta^N = 1 - \epsilon$ given by S. S. Wilks [1]. A direct numerical solution of (1) by trial requires rather laborious tabulations. An approximate formula for the solution has been indicated by H. Scheffe and J. W. Tukey [2], however an analytic proof for this approximation does not seem to be available. The present note describes a graph which makes it possible to solve (1) with sufficient accuracy for all practically useful values of $\beta$ and $\epsilon$.


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Z. W. Birnbaum. H. S. Zuckerman. "A Graphical Determination of Sample Size for Wilks' Tolerance Limits." Ann. Math. Statist. 20 (2) 313 - 316, June, 1949.


Published: June, 1949
First available in Project Euclid: 28 April 2007

zbMATH: 0041.26101
MathSciNet: MR30176
Digital Object Identifier: 10.1214/aoms/1177730044

Rights: Copyright © 1949 Institute of Mathematical Statistics

Vol.20 • No. 2 • June, 1949
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