Simultaneous Confidence Intervals for All Pairwise Differences between Medians of Zero-Inflated Lognormal Distributions

Changes in rainfall across different regions hold significance due to their substantial impact on daily life. Rainfall data is generally thought to have a lognormal distribution. Because there are some days with no rain, a zero-inflated lognormal distribution is more suited to accurately modeling the data. Therefore, the objective of this research is to establish simultaneous confidence intervals for all pairwise differences between the medians of the zero-inflated lognormal distributions using five methods: generalized confidence interval, fiducial generalized confidence interval, method of variance estimates recovery, highest posterior density using Jeffreys prior, and highest posterior density using Jeffreys rule prior. Coverage probabilities and expected lengths are employed to compare the efficiency of these methods. The overall study results indicate that the highest posterior density interval demonstrates the highest efficacy. Additionally, this result is further affirmed through its application to precipitation data in Thailand.