Tolerance limits under zero-inflated lognormal and gamma distributions

The computation of upper tolerance limits is investigated for the zero-inflated lognormal distribution and the zero-inflated gamma distribution, with or without covariates. The methodologies investigated consist of a fiducial approach and bootstrap approaches, including the bias corrected and accelerated bootstrap and a bootstrap-calibrated delta method. Based on estimated coverage probabilities, it is concluded that overall, the bootstrap-calibrated delta method is to be preferred for computing the upper tolerance limit. Two applications are also discussed; the first application is on the analysis of data on health care expenditures, and the second application is on testing the safety of body armor.