Generalized confidence interval for the common coefficient of variation of several zero-inflated Birnbaum-Saunders distributions with an application to wind speed data

Usanee Janthasuwan; Suparat Niwitpong; Sa-Aat Niwitpong; Usanee Janthasuwan; Suparat Niwitpong; Sa-Aat Niwitpong

doi:10.3934/math.2025127

AIMS Mathematics

2025, Volume 10, Issue 2: 2697-2723. doi: 10.3934/math.2025127

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Generalized confidence interval for the common coefficient of variation of several zero-inflated Birnbaum-Saunders distributions with an application to wind speed data

Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand

Received: 12 December 2024 Revised: 22 January 2025 Accepted: 06 February 2025 Published: 14 February 2025
MSC : 62F25, 62P12

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.
- average width,
- confidence interval,
- coefficient of variation,
- coverage probability,
- zero-inflated Birnbaum-Saunders,
- wind speed
Citation: Usanee Janthasuwan, Suparat Niwitpong, Sa-Aat Niwitpong. Generalized confidence interval for the common coefficient of variation of several zero-inflated Birnbaum-Saunders distributions with an application to wind speed data[J]. AIMS Mathematics, 2025, 10(2): 2697-2723. doi: 10.3934/math.2025127

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Abstract

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.

References

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