Confidence Intervals for the Difference between Two Coefficients of Variation of the delta-Birnbaum-Saunders Distributions

The delta-Birnbaum-Saunders distribution is a relatively novel concept that combines the Birnbaum-Saunders with the binomial distributions. As a result, datasets containing both positive and zero values conform well with this distribution, making it particularly intriguing. Additionally, coefficients of variation are among the important statistics for comparing the dispersion of data. Therefore, there is an interest in proposing methods for constructing confidence intervals, which play a crucial role in statistical inference for the difference between two coefficients of variation in delta-Birnbaum-Saunders distributions. There are four methods proposed: the method of variance estimates recovery, the bootstrap confidence interval, the generalized confidence interval based on the variance stabilized transformation, and the generalized confidence interval based on the Wilson score method. All the methods are compared in terms of performance using coverage probability and average width through Monte Carlo simulations. The simulation results show that the bootstrap confidence interval performs similarly to the method of variance estimate recovery, except in cases where the shape parameter is large. In addition, it is shown that the generalized confidence interval based on variance stabilized transformation and the generalized confidence interval based on the Wilson score method yield similar results and demonstrate the highest efficiency compared to other methods. Finally, two datasets are used to illustrate the application of the proposed confidence intervals.