Best prediction regions for future exponential record intervals

Abstract

A class of prediction regions for a future upper record interval $(R_s,R_l)$ based on a type-II censored sample from the exponential distribution is presented in this paper. The best prediction region for $(R_s,R_l)$ is then determined by solving a constrained nonlinear optimization problem. The objective function is the area of the prediction region and the constraints are related to the desired confidence level. According to our approach, it suffices to simultaneously solve four nonlinear equations for deriving the prediction region with minimal area. To show the usefulness of our results, we present a simulation study. Three practical studies regarding times between consecutive telephone calls, lifetimes to breakdown of insulating fluids and annual rainfalls recorded at Los Angeles Civic Center are provided for comparing conservative and optimal prediction regions. In most cases, the reduction in area is appreciable. Finally, some applications and extensions are also pointed out.

Keywords:

• Constrained optimization
• exponential distribution
• prediction region
• record data
• type-II censored data

2010 Mathematics Subject Classifications:

• 62N05
• 62N01
• 62F30

Acknowledgments

The authors would like to thank the referees for their careful reading and constructive comments which improved the paper.

Disclosure statement

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

Additional information

Funding

The work of the second author was partially supported by the Ministry of Science and Innovation (MICINN) of Spain under Grant PID2019-110442GB-I00.