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Abstract:
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This presentation develops the computation of upper tolerance limits under zero-inflated log-normal and zero-inflated gamma distributions. Models without covariates and with covariates are separately considered, and point-wise upper tolerance limits are derived under models with covariates. For the zero-inflated log-normal model, techniques used to calculate the tolerance limits include generalized pivotal quantities (GPQs), fiducial quantities, the bootstrap, and the delta method with a bootstrap calibration. Numerical results indicate that the GPQ methodology and the bootstrap calibration of the delta method provide very satisfactory performance. For the zero-inflated gamma model, tolerance limits are calculated based on bootstrapping a pivot-like statistic, and based on the bootstrap calibration of the delta method. Numerical results indicate satisfactory performance for these methods. The results are applied to a variety of zero-inflated data sets: health expenditure data and body armor protection data.
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