Two-sided tolerance intervals for members of the (log)-location-scale family of distributions

Abstract

In this paper, we propose methods to calculate exact factors for two-sided control-the-centre and control-both-tails tolerance intervals for the (log)-location-scale family of distributions, based on complete or Type II censored data. With Type I censored data, exact factors do not exist. For this case, we developed an algorithm to compute approximate factors. Our approaches are based on Monte Carlo simulations. We also provide algorithms for computing TIs that control the probability in both tails of a distribution. A simulation study for Type I censored data shows that the estimated coverage probability is close to the nominal confidence level when the expected number of uncensored observations is moderate to large. We illustrate the methods with applications using different combinations of distributions and types of censoring.

Keywords:

• Censored data
• lognormal
• maximum likelihood
• Monte-Carlo simulation
• pivotal quantity
• Weibull

Acknowledgements

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

Notes

No potential conflict of interest was reported by the authors.