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Two‐Sided Tolerance Limits with Two‐Stage Sampling from Normal Populations—Monte Carlo Studies of the Distribution of Coverages
Author(s) -
Seeger Paul,
Thorsson Ulf
Publication year - 1973
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2346778
Subject(s) - monte carlo method , statistics , mathematics , stage (stratigraphy) , sampling (signal processing) , statistical physics , physics , biology , optics , detector , paleontology
Summary 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.