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December, 1948 Non-Parametric Tolerance Limits
R. B. Murphy
Ann. Math. Statist. 19(4): 581-589 (December, 1948). DOI: 10.1214/aoms/1177730154


In this note are presented graphs of minimum probable population coverage by sample blocks determined by the order statistics of a sample from a population with a continuous but unknown cumulative distribution function (c.d.f.). The graphs are constructed for the three tolerance levels .90, .95, and .99. The number, $m$, of blocks excluded from the tolerance region runs as follows: $m$ = 1(1)6(2)10(5)30(10)60(20)100, and the sample size, $n$, runs from $m$ to 500. Thus the curves show the solution, $\beta$, of the equation $1 - \alpha = I_\beta(n - m + 1, m)$ for $\alpha = .90, .95, .99$ over the range of $n$ and $m$ given above, where $I_x(p, q)$ is Pearson's notation for the incomplete beta function. Examples are cited below for the one- and two-variate cases. Finally, the exact and approximate formulae used in computations for these graphs are given.


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R. B. Murphy. "Non-Parametric Tolerance Limits." Ann. Math. Statist. 19 (4) 581 - 589, December, 1948.


Published: December, 1948
First available in Project Euclid: 28 April 2007

zbMATH: 0032.29406
MathSciNet: MR28095
Digital Object Identifier: 10.1214/aoms/1177730154

Rights: Copyright © 1948 Institute of Mathematical Statistics

Vol.19 • No. 4 • December, 1948
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