Simultaneous Fiducial Generalized Confidence Intervals for Ratios of Means of Lognormal Distributions

Abstract

In this paper, we construct Fiducial Generalized Confidence Intervals (FGCI) for ratio of means of two lognormal distributions based on independent observations from the two distributions. We compared the proposed method with another method, the Z-Score method. A simulation study showed that the FGCI method performs much better than the Z-Score method, especially for small and medium samples. We also prove that the confidence intervals constructed using FGCI method have correct asymptotic coverage. In this paper we propose a new method for constructing simultaneous confidence intervals for all pairwise ratios of means of lognormal distributions. Our approach is based on Fiducial Generalized Pivotal Quantities (FGPQ) for vector parameters. Simulation studies show that the constructed confidence intervals have satisfactory small sample performance. We also prove that they have correct asymptotic coverage. The result has applications in bioequivalence studies for comparing three or more drug formulations.