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

K. Krishnamoorthy, Dustin Waguespack and Ngan Hoang-Nguyen-Thuy

Journal of Applied Statistics, 2020, vol. 47, issue 1, 160-175

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.

Date: 2020
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DOI: 10.1080/02664763.2019.1634681

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