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Abstract One-sided tolerance limits are developed for the three-parameter generalized gamma distribution of Stacy, one parameter at a time being assumed unknown. This distribution includes the exponential, gamma, and Weibull distributions as special cases. Confidence limits for the unknown parameter are also given in each case. Limits are developed based on the statistic and also on the r-th order statistic. The limits based on a single order statistic take into account the distributional form of the variable and are not the familiar nonparametric tolerance limits of Wilks which do not depend on the functional form of the variable. Some comparisons of the limits are considered in special cases and also some of the limits are shown to satisfy the “most stable” criterion of Goodman and Madansky.
Bain et al. (Wed,) studied this question.