Confidence Intervals for Ratios of the Coefficients of Variation of the Delta-Birnbaum-Saunders Distributions

The Delta-Birnbaum-Saunders distribution is a combination of positive values that follow the Birnbaum-Saunders distribution and zeros that follow the binomial distribution, making it a relatively new distribution. The coefficient of variation is calculated as the ratio of the standard deviation to the mean. It is important for comparing the dispersion of datasets. Therefore, this paper aims to generate confidence intervals for ratios of coefficients of variation under the Delta-Birnbaum-Saunders distributions. We have proposed four methods for constructing confidence intervals, namely, 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. The assessment of their performance relies on coverage probabilities and average widths obtained through Monte Carlo simulations. The overall study results reveal that the generalized confidence interval based on the variance stabilized transformation and the generalized confidence interval based on the Wilson score methods provide similar values in both the coverage probabilities and average widths, making them the two most efficient methods. Furthermore, it was found that the method of variance estimates recovery performs well when the shape parameters are small. Finally, all the proposed methods will be applied to wind speed data in Thailand.