Confidence interval, prediction interval and tolerance limits for a two-parameter Rayleigh distribution

ABSTRACT

The problems of interval estimating the parameters and the mean of a two-parameter Rayleigh distribution are considered. We propose pivotal-based methods for constructing confidence intervals for the mean, quantiles, survival probability and for constructing prediction intervals for the mean of a future sample. Pivotal quantities based on the maximum likelihood estimates (MLEs), moment estimates (MEs) and the L-moments estimates (L-MEs) are proposed. Interval estimates based on them are compared via Monte Carlo simulation. Comparison studies indicate that the results based on the MEs and the L-MEs are very similar. The results based on the MLEs are slightly better than those based on the MEs and the L-MEs for small to moderate sample sizes. The methods are illustrated using an example involving lifetime data.

Keywords:

• Confidence interval
• moment estimates
• prediction interval
• precision
• quantile estimation
• tolerance interval

Acknowledgements

The authors are grateful to two reviewers for providing valuable comments and suggestions which enhanced the first version of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.