Two‐Sided Tolerance Limits with Two‐Stage Sampling from Normal Populations—Monte Carlo Studies of the Distribution of Coverages

Paul Seeger and Ulf Thorsson

Journal of the Royal Statistical Society Series C, 1973, vol. 22, issue 3, 292-300

Abstract: When Wald–Wolfowitz's approximate method of computing tolerance intervals is applied to two‐stage sampling from a normal population further approximations have to be introduced. Their effect on the confidence of the intervals has been studied by computer simulation experiments presented in this paper. The approximation seems to be acceptable when the number of sampled secondary units per primary unit is 2 but not when it is 5 or more. Equivalent results are obtained for a distribution with a slightly negative kurtosis. For a skew distribution the approximation gives poor results. The distribution of the actual proportion of the population that is enclosed in the interval is also obtained.

Date: 1973
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