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TWO-SIDED TOLERANCE LIMITS FOR NORMAL POPULATIONS--SOME IMPROVEMENTS.
- Source :
-
Journal of the American Statistical Association . Jun69, Vol. 64 Issue 326, p610. 11p. - Publication Year :
- 1969
-
Abstract
- Ellison has shown that the Wald-Wolfowitz tolerance limits for a normal distribution, x + lambda s, are good only to 0(n/N[sup 2]), rather than to 0(1/N[sup 2]). Here x is distributed normally with mean mu and variance sigma[sup 2]/N while s[sup 2]/sigma[sup 2] is distributed as chi[sup 2, sub n]/n independently of x. Thus, for n much greater than N[sup 2] the usual values of lambda are incorrect; Ellison has proposed an alternative in this case. This paper derives new lambda's which have two advantages over the Wald-Wolfowitz and the Ellison limits. First, they are shown to be better approximations. Secondly, they are easily calculated in the sense that only tables of the normal and chi[sup 2] distributions are required and the solution of a non-linear equation is not required. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01621459
- Volume :
- 64
- Issue :
- 326
- Database :
- Academic Search Index
- Journal :
- Journal of the American Statistical Association
- Publication Type :
- Academic Journal
- Accession number :
- 4602015
- Full Text :
- https://doi.org/10.2307/2283644