Confidence intervals for coefficient of variation of Delta-Birnbaum-Saunders distribution with application to wind speed data

Abstract

The delta-Birnbaum-Saunders distribution is considered a relatively new distribution that combines the Birnbaum-Saunders distribution with data that include zero values. Furthermore, the coefficient of variation is important because it provides a standardized measure of relative variability that can be calculated from the ratio of the standard deviation to the mean. Consequently, this study focuses on constructing confidence intervals for the coefficient of variation of the delta-Birnbaum-Saunders distribution. We have proposed three methods for constructing confidence intervals: the generalized confidence interval based on the variance-stabilized transformation, the generalized confidence interval based on the Wilson score method, and the normal approximation compared with the bootstrap confidence interval. The performance of all these methods was compared using coverage probabilities and expected lengths through Monte Carlo simulations using the R statistical software, and various parameters were comprehensively specified. The study results revealed that the generalized confidence interval based on the variance stabilized transformation and the generalized confidence interval based on the Wilson score method provided similar results and were the best-performing methods. Additionally, the study results show that as the sample size increases, all methods tend to become more effective. Finally, we applied all the methods presented to wind speed data from Ubon Ratchathani province and Si Sa Kat province in Thailand.

Keywords

• bootstrap confidence interval
• coefficient of variation
• delta-birnbaum-saunders
• generalized confidence interval
• normal approximation