Confidence Intervals for the Median of the Delta-Lognormal Distribution with Application

A median is a crucial descriptive statistic for determining the midpoint of a dataset. Hence, we propose new confidence intervals (CIs) for the median of the delta-lognormal distribution using the methods of FGCI, MOVER, HPD-J, and HPD-JR. The CPs and ELs were used to evaluate the effectiveness of the proposed CIs. All the approaches were assessed via Monte Carlo simulation. The research results demonstrate that the FGCI has CPs that are always very similar to the nominal confidence level, although its expected lengths are relatively wide and begin to shorten as the sample size grows. Comparing various CIs, the HPD-J performs the best overall. Finally, all the methods considered are illustrated using datasets of rainfall amounts in Thailand.