Confidence intervals for coefficient of variation of Delta-Birnbaum-Saunders distribution with application to wind speed data
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...
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241631 |
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| author | Usanee Janthasuwan Suparat Niwitpong Sa-Aat Niwitpong |
| author_facet | Usanee Janthasuwan Suparat Niwitpong Sa-Aat Niwitpong |
| author_sort | Usanee Janthasuwan |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d87f54ecadb54f4baac32bafa76a1125 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
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| series | AIMS Mathematics |
| spelling | doaj-art-d87f54ecadb54f4baac32bafa76a11252025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912342483426910.3934/math.20241631Confidence intervals for coefficient of variation of Delta-Birnbaum-Saunders distribution with application to wind speed dataUsanee Janthasuwan0Suparat Niwitpong1Sa-Aat Niwitpong2Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, ThailandDepartment of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, ThailandDepartment of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, ThailandThe 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.https://www.aimspress.com/article/doi/10.3934/math.20241631bootstrap confidence intervalcoefficient of variationdelta-birnbaum-saundersgeneralized confidence intervalnormal approximation |
| spellingShingle | Usanee Janthasuwan Suparat Niwitpong Sa-Aat Niwitpong Confidence intervals for coefficient of variation of Delta-Birnbaum-Saunders distribution with application to wind speed data AIMS Mathematics bootstrap confidence interval coefficient of variation delta-birnbaum-saunders generalized confidence interval normal approximation |
| title | Confidence intervals for coefficient of variation of Delta-Birnbaum-Saunders distribution with application to wind speed data |
| title_full | Confidence intervals for coefficient of variation of Delta-Birnbaum-Saunders distribution with application to wind speed data |
| title_fullStr | Confidence intervals for coefficient of variation of Delta-Birnbaum-Saunders distribution with application to wind speed data |
| title_full_unstemmed | Confidence intervals for coefficient of variation of Delta-Birnbaum-Saunders distribution with application to wind speed data |
| title_short | Confidence intervals for coefficient of variation of Delta-Birnbaum-Saunders distribution with application to wind speed data |
| title_sort | confidence intervals for coefficient of variation of delta birnbaum saunders distribution with application to wind speed data |
| topic | bootstrap confidence interval coefficient of variation delta-birnbaum-saunders generalized confidence interval normal approximation |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241631 |
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