A Graphical Determination of Sample Size for Wilks' Tolerance Limits
Birnbaum, Z. W. ; Zuckerman, H. S.
Ann. Math. Statist., Tome 20 (1949) no. 4, p. 313-316 / Harvested from Project Euclid
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 $\epsilon$.
Publié le : 1949-06-14
Classification: 
@article{1177730044,
     author = {Birnbaum, Z. W. and Zuckerman, H. S.},
     title = {A Graphical Determination of Sample Size for Wilks' Tolerance Limits},
     journal = {Ann. Math. Statist.},
     volume = {20},
     number = {4},
     year = {1949},
     pages = { 313-316},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177730044}
}
Birnbaum, Z. W.; Zuckerman, H. S. A Graphical Determination of Sample Size for Wilks' Tolerance Limits. Ann. Math. Statist., Tome 20 (1949) no. 4, pp.  313-316. http://gdmltest.u-ga.fr/item/1177730044/