The log-normal distribution (skewed distribution or asymmetry distribution) is used to describe random variables comprising positive real values. It is well known that the logarithm values of these are normally distributed (symmetry distribution). Positively right-skewed data applicable to the log-normal distribution are frequently observed in the fields of environmental studies, biology, and medicine. The number of zero observations follows a binomial distribution. However, problems can arise in the analysis of data containing zero observations along with log-normally distributed data, for which the delta-lognormal distribution is often referred to for using the analysis of the data. In statistics, the percentile provides the relative standing of a numerical data point when compared to all of the others in a distribution with reference to the observations at or below it. In this study, estimates for the confidence interval for the ratio of the percentiles of two delta-lognormal distributions are constructed using fiducial generalized confidence interval approaches based on the fiducial quantity and the optimal generalized fiducial quantity, the Bayesian approach, and the parametric bootstrap method. As assessed by Monte Carlo simulations using the RStudio programming in terms of the coverage probability and the average length, the Bayesian approach performed quite well by providing adequate coverage probabilities along with the shortest average lengths in all of the scenarios tested. Daily rainfall data contain both zero and positive values. The daily rainfall data can usually be fitted to the delta-lognormal distribution. Their application to rainfall data is also provided to illustrate their efficacies with real data. The efficacy of the approach is used to compare two rainfall dispersion populations.

Delta Birnbaum–Saunders distribution has both zero and positive values, with positive values following a Birnbaum–Saunders distribution and zero observations following a binomial distribution. This study constructs a confidence interval for the percentile of the Delta Birnbaum–Saunders distribution using the generalized confidence interval approach and compares it with the bootstrap approach, the highest posterior density approach based on the bootstrap method, the Bayesian approach, and the highest posterior density approach based on the Bayesian method. Monte Carlo simulations are used to evaluate the performance of these confidence intervals. The results show that the generalized confidence interval approach is effective for constructing CIs for the percentiles of the Delta Birnbaum–Saunders distribution. Additionally, when the sample size is large, both the Bayesian approach and the highest posterior density approach based on the Bayesian method are viable alternatives. These approaches are demonstrated using daily wind speed data in Prachin Buri province, Thailand.

This paper develops simultaneous confidence intervals (SCIs) for pairwise differences of means with zero-inflated Rayleigh (ZIR) distributions, a flexible framework for modeling positively skewed data with excess zeros. Closed-form expressions for the ZIR mean are derived, and several competing interval estimation procedures are investigated, including generalized confidence interval (GCI), parametric bootstrap (PB), method of variance estimates recovery (MOVER), delta-method normal approximation, and highest posterior density (HPD) intervals. The finite-sample performance of the proposed SCIs is examined via extensive Monte Carlo simulations, focusing on empirical coverage probabilities (CPs) and average interval lengths (ALs) over a broad range of parameter configurations and zero-inflation levels. A real data application to road accident fatality counts demonstrates the practical utility of the proposed methodology. The results show that the HPD method consistently achieves the most favorable balance between coverage accuracy and interval efficiency. Overall, this study advances reliable simultaneous inference for zero-inflated models commonly encountered in environmental, biomedical, and reliability studies.