Asymptotic and Bootstrap Confidence Intervals for the Ratio of Modes of Log-normal Distributions

The log-normal distribution is essential for modeling positively skewed life-time data. Consequently, the log-normal distribution is used in numerous real-world situations. As a measure of central tendency, the mode corresponds to the most typical value within the data set. The goal of this paper is to estimate the confidence intervals (CIs) for the ratios of modes of two log-normal distributions using the asymptotic confidence interval ( CI_Asym ) and three varieties of bootstrap confidence intervals ( CI_t-boot,CI_p-boot , and CI_s-boot ). The effectiveness of the proposed CI methods is evaluated in terms of their coverage probabilities and average widths via Monte Carlo simulation. Lastly, the proposed CI methods were evaluated by applying them to real-world data on PM2.5 mass concentration in two areas of Thailand.