Tolerance limits under zero‐inflated lognormal and gamma distributions

Abstract

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.

Bayesian estimation for the mean of delta-gamma distributions with application to rainfall data in Thailand

“…Inference from a delta-gamma distribution applied to real data has been conducted in many fields. For instance, the testing of body armor for stab resistance in engineering during which a zero value was recorded when the armor was not pierced ( Zimmer, Park & Mathew, 2020 ) and ecological data for biomasses that often contain a high proportion of zeros with skewed positive values ( Lecomte et al, 2013 ).…”

“…The confidence interval is a range of observed values within which an unknown population parameter value such as the population mean is known to reside, and a specific confidence level is applied to conclude that the estimated interval contains the true value of the parameter. As an example, Zimmer, Park & Mathew (2020) estimated the coverage probabilities of the 95% upper confidence limits of a zero-inflated gamma distribution for confidence intervals constructed via bias-corrected and accelerated bootstrapping and the bootstrap-calibrated delta method.…”