Confidence intervals for a ratio of percentiles of location-scale distributions

The problem of estimating a ratio of percentiles of two independent location-scale distributions is considered. A fiducial approach is proposed and described in details for the normal, lognormal, two-parameter exponential and Weibull distributions. For the normal case, the fiducial confidence intervals (CIs) turn out to be exact when the variances are equal. Procedures for constructing CIs for ratio of percentiles involving two-parameter exponential distributions and Weibull distributions are given with computational details. The fiducial methods can be readily extended to the case where the samples are type II censored. The methods are illustrated using real-world data sets.& COPY; 2023 Elsevier B.V. All rights reserved.