Prediction intervals for future Weibull residual data

Abstract

In reliability theory, risk analysis, renewal processes and actuarial studies, the residual lifetimes data play an important essential role in studying the conditional tail of the lifetime data. In this paper, based on some observed ordered residual Weibull data, we introduce different prediction methods for obtaining prediction intervals (PIs) of future residual lifetimes including likelihood, Wald, moments, parametric bootstrap, and highest conditional methods. Monte Carlo simulations are performed to compare the performances of the so obtained PIs and one data analysis is performed for illustration purposes.

Keywords:

• Weibull distribution
• residual lifetimes
• order statistics
• prediction interval

AMS Subject Classification (2010):

• 62G30
• 62F10
• 62F15

Acknowledgements

We would like to thank the editor for his encouragement and the referees for their valuable suggestions and comments. We appreciate one of the referees for bringing Theorem 9.3.2 of Casella and Berger [24] to our attention.

Disclosure statement

No potential conflict of interest was reported by the authors.