A general algorithm for computing simultaneous prediction intervals for the (log)-location-scale family of distributions

ABSTRACT

Making predictions of future realized values of random variables based on currently available data is a frequent task in statistical applications. In some applications, the interest is to obtain a two-sided simultaneous prediction interval (SPI) to contain at least k out of m future observations with a certain confidence level based on n previous observations from the same distribution. A closely related problem is to obtain a one-sided upper (or lower) simultaneous prediction bound (SPB) to exceed (or be exceeded) by at least k out of m future observations. In this paper, we provide a general approach for computing SPIs and SPBs based on data from a particular member of the (log)-location-scale family of distributions with complete or right censored data. The proposed simulation-based procedure can provide exact coverage probability for complete and Type II censored data. For Type I censored data, our simulation results show that our procedure provides satisfactory results in small samples. We use three applications to illustrate the proposed simultaneous prediction intervals and bounds.

KEYWORDS:

• Censored data
• coverage probability
• k out of m
• lognormal
• simulation
• Weibull

Acknowledgments

The authors thank the editor, an associate editor, and two referees, for their valuable comments and suggestions that helped us to improve this paper. The authors acknowledge Advanced Research Computing at Virginia Tech for providing computational resources.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work by Hong was partially supported by the National Science Foundation Grant CNS-1565314 to Virginia Tech.