Open AccessTolerance limits under zero‐inflated lognormal and gamma distributions
Author(s) -
Zimmer Zachary,
Park DoHwan,
Mathew Thomas
Publication year - 2021
Publication title -
computational and mathematical methods
Language(s) - English
Resource type - Journals
ISSN - 2577-7408
DOI - 10.1002/cmm4.1113
Subject(s) - log normal distribution , zero (linguistics) , mathematics , statistics , econometrics , gamma distribution , statistical physics , physics , linguistics , philosophy
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.