Empirical likelihood inference for the mean past lifetime function

Abstract

In survival analysis and reliability theory, the mean past lifetime (MPL), arises in situations where the mean time elapsed since the failure of a component T, given that it has failed before time t, is of interest. For inference on the MPL function, some procedures have been proposed in the literature for the MPL function's estimator. In this paper, an empirical likelihood (EL) inference procedure of the MPL function is developed. In addition to that, we obtain the adjusted EL and mean EL confidence interval for the MPL function. The EL confidence intervals are compared through extensive simulation studies in terms of coverage probability and the average length of the confidence interval. The simulation studies showed that the proposed EL methods have better coverage probability and shorter average lengths than the normal approximation results. Finally, the proposed methods are illustrated by two real data analyses.

Keywords:

• Confidence interval
• estimating equation
• empirical likelihood
• adjusted empirical likelihood
• mean empirical likelihood
• Wilks' theorem

2020 Mathematics Subject Classification:

• 62G15

Acknowledgements

We would like to thank the Editor-in-Chief Professor Meister, an AE, and two reviewers for their constructive comments and insightful suggestions, which led to the significant improvement of the paper.

Disclosure statement

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

Additional information

Funding

Dr. Yichuan Zhao thanks the grant supports under the Simons Foundation [grant number 638679] and the National Security Agency [grant number H89230-20-1-0020].