Confidence Intervals for the Difference and Ratio of Two Variances of Delta–Inverse Gaussian Distributions

Accurate statistical inference for zero-inflated and highly skewed data requires confidence interval procedures with a strong finite-sample performance. The delta–inverse Gaussian distribution provides a flexible framework for modeling such data by combining a point mass at zero with an inverse Gaussian distribution for positive observations, making it suitable for application in various fields such as traffic mortality, insurance, and environmental studies. This paper develops and compares several confidence interval estimation methods for the difference and the ratio of two variances from independent delta–IG distributions. The proposed approaches include adjusted generalized confidence intervals, fiducial confidence intervals, Bayesian credible intervals, the method of variance estimates recovery, and normal approximation methods used as benchmarks. The finite-sample performance of these methods is evaluated through Monte Carlo simulations under various parameter configurations and both balanced and unbalanced sample sizes, with an emphasis on coverage probability and interval width. The simulation results show that AGCI and MOVER generally achieve coverage probabilities close to the nominal level while producing relatively narrow intervals. The MOVER performs particularly well when zero-inflation probabilities are equal, whereas AGCI is more effective when they differ. Illustrative real-data examples are provided to demonstrate practical implementations.