Wind speed is a critical factor that affects various aspects of life in Thailand, particularly agriculture, which is a fundamental component of the Thai economy. Therefore, studying and understanding wind speed is essential for planning and developing the country's economy sustainably. Wind speed data often include both positive and zero values, which are consistent with the zero-inflated Birnbaum-Saunders distribution. Additionally, the inherent variability of wind speed poses challenges for accurate prediction. When analyzing data from multiple weather stations, the common coefficient of variation helps compare the wind variability at each station, even if the average wind speeds differ. Therefore, the estimation of the common coefficient of variation allows for reliable statistical inference and decision-making. In this article, we proposed five methods to construct confidence intervals for the common coefficient of variation of several zero-inflated Birnbaum-Saunders distributions. These methods include the generalized confidence interval, the method of variance estimation recovery, the large sample approximation, the bootstrap confidence interval, and the fiducial generalized confidence interval. We evaluated the performance of these methods using a comprehensive simulation study and compared them in terms of coverage probabilities and average widths. The results revealed that overall, the generalized confidence interval and the bootstrap confidence interval are the most effective and perform better than other methods in various situations. Finally, we applied these proposed methods to wind speed data from Thailand.

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.

The data used for the analysis were collected from multiple regions or years. Evaluating each region or year separately may be insufficient for drawing comprehensive inferences and may fail to reveal statistically significant differences. To ensure the reliability of the analysis and to enable overall conclusions, it is necessary to apply a statistical method known as simultaneous confidence intervals. This technique enables the simultaneous construction of confidence intervals for multiple parameters. Therefore, we proposed and evaluated methods for constructing simultaneous confidence intervals for all pairwise differences between the coefficients of variation in zero-inflated Birnbaum-Saunders distributions. The methods utilized for constructing simultaneous confidence intervals comprise the generalized confidence interval (GCI), the bootstrap confidence interval (BCI), the method of variance estimates recovery (MOVER), the MOVER based on GCI, the MOVER based on BCI, the Bayesian credible interval, and the highest posterior density interval (HPD). Monte Carlo simulations were employed to evaluate the performance of each method, which involved the assessment of coverage probabilities and average widths under a set of parameter configurations and sample sizes. The generalized confidence interval method was the most efficient overall, as indicated by the simulation results. Finally, all proposed methods were applied to real-world wind speed data to examine their practical applicability and to demonstrate the consistency of the results between the simulation study and real-world applications.