Confidence Intervals for the Ratio of Means of Delta-Lognormal Distribution

Abstract

This paper investigates confidence intervals for the ratio of means in the delta-lognormal distribution. The method of variance estimates recovery (MOVER) based on the variance stabilizing transformation, Wilson score method and Jeffreys method were proposed to establish confidence intervals for the ratio of delta-lonormal means. These confidence intervals were compared with the existing confidence interval based on the generalized confidence interval (GCI). The coverage probabilities and average lengths were the performance of these proposed confidence intervals which were evaluated via Monte Carlo simulation. The simulation results showed that the three MOVERs’ performance is similar to the GCI in terms of coverage probability for all sample sizes except when the probability \(\delta \) of having zero is close to zero and the coefficient of variation gets large. However, the MOVER based on Jeffreys provides the minimal average lengths when the coefficient of variation are small for all sample sizes. Finally, two data sets are used to illustrate examples of using the proposed confidence intervals.