Estimation Methods for the Difference and Ratio of the Variances of Birnbaum–Saunders Distributions Containing Zero Values and Application to Wind Speed Data

Wind energy, occurring naturally, is a clean and renewable energy source that does not harm the environment. It can be harnessed endlessly, making it a valuable resource. Therefore, wind energy has been put to good use. Electricity through wind turbines can help reduce carbon and greenhouse gases from electricity production. Wind energy occurs naturally, but there may be uneven wind speeds. This inconsistency affects electricity production, as it requires a consistent speed. Consequently, we have identified a need to investigate wind speed to utilize wind energy for electricity production efficiently. The daily wind speed can be approximated using confidence intervals for the difference and ratio between the variances of the Birnbaum–Saunders distributions containing zero values. Thus, we constructed them by using generalized confidence interval (GCI), generalized fiducial confidence interval (GFCI), the method of variance estimates recovery (MOVER), and normal approximation (NA). Specifically, we apply GCI and GFCI while considering the estimation of delta using the Variance Stabilized Transformation (VST), Wilson, and Hannig methods. By comparison, the performance measures for all methods, the coverage probability (CP), and average width (AW) were assessed via Monte Carlo simulation in the R statistical software. The results of the Monte Carlo simulation studies show that for estimating the confidence interval of the difference and ratio between the variances, the GFCI based on the Hannig method is close to the nominal confidence level and yields shorter intervals than the other methods. Except in the case of estimating the confidence interval of the difference of variances when the sample sizes are equal, the results of the study are as follows: For small samples, GCI based on the Wilson method was found to be more effective, while in large samples, the GFCI based on the VST method was found to be the most effective. To illustrate the efficacy of our proposed methods, we applied them to the daily wind speed data from Pattaya station and Laem Chabang station, Chonburi Province, Thailand.