Simultaneous confidence intervals for ratios of means of zero-inflated log-normal populations

Abstract

This paper studies simultaneous confidence intervals (SCIs) for the ratios of means of zero-heavy log-normal populations. We propose four SCIs by using the Bonferroni adjustment principle. Specifically, we integrate the fiducial generalized pivotal quantity (FGPQ) with the other two statistics to have two FGPQ-based methods and incorporate the variance estimates recovery (MOVER) with FGPQ to have two MOVER-based methods. We develop expedient algorithms to implement the methods, and conduct extensive simulation studies to evaluate and compare the performance of the four methods, which show that our methods perform well. We also apply the methods to analyse a real data set as an illustration.

Keywords:

• Bonferroni adjustment
• fiducial generalized pivotal quantity (FGPQ)
• log-normal
• method of variance estimates recovery (MOVER)

Acknowledgements

Qi Zhang and Jing Xu contributed equally to this work. The authors would like to sincerely thank the Editor, Associate Editor, and anonymous reviewers for their constructive and insightful comments, which significantly improved the presentation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of Zhang and Li was supported by grant 11871294 from National Natural Science Foundation of China. Liang's research was partially supported by NSF grant DMS-1620898.