Confidence Intervals for Comparing the Variances of Two Independent Birnbaum–Saunders Distributions
Fatigue in a material occurs when it is subjected to fluctuating stress and strain, which usually results in failure due to the accumulated damage. In statistics, asymmetric distribution, which is commonly used for describing the fatigue life of materials, is the Birnbaum–Saunders (BS) distribution....
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/7/1492 |
| _version_ | 1797433040122675200 |
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| author | Wisunee Puggard Sa-Aat Niwitpong Suparat Niwitpong |
| author_facet | Wisunee Puggard Sa-Aat Niwitpong Suparat Niwitpong |
| author_sort | Wisunee Puggard |
| collection | DOAJ |
| description | Fatigue in a material occurs when it is subjected to fluctuating stress and strain, which usually results in failure due to the accumulated damage. In statistics, asymmetric distribution, which is commonly used for describing the fatigue life of materials, is the Birnbaum–Saunders (BS) distribution. This distribution can be transform to the normal distribution, which is symmetrical. Furthermore, variance is used to examine the dispersion of the fatigue life data. However, comparing the variances of two independent samples that follow BS distributions has not previously been reported. To accomplish this, we propose methods for providing the confidence interval for the ratio of variances of two independent BS distributions based on the generalized fiducial confidence interval (GFCI), a Bayesian credible interval (BCI), and the highest posterior density (HPD) intervals based on a prior distribution with partial information (HPD-PI) and a proper prior with known hyperparameters (HPD-KH). A Monte Carlo simulation study was carried out to examine the efficacies of the methods in terms of their coverage probabilities and average lengths. The simulation results indicate that the HPD-PI performed satisfactorily for all sample sizes investigated. To illustrate the efficacies of the proposed methods with real data, they were also applied to study the confidence interval for the ratio of the variances of two 6061-T6 aluminum coupon fatigue-life datasets. |
| first_indexed | 2024-03-09T10:11:29Z |
| format | Article |
| id | doaj.art-5ec8357bb0e646f489e32d4092fb062a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T10:11:29Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-5ec8357bb0e646f489e32d4092fb062a2023-12-01T22:45:05ZengMDPI AGSymmetry2073-89942022-07-01147149210.3390/sym14071492Confidence Intervals for Comparing the Variances of Two Independent Birnbaum–Saunders DistributionsWisunee Puggard0Sa-Aat Niwitpong1Suparat 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, ThailandFatigue in a material occurs when it is subjected to fluctuating stress and strain, which usually results in failure due to the accumulated damage. In statistics, asymmetric distribution, which is commonly used for describing the fatigue life of materials, is the Birnbaum–Saunders (BS) distribution. This distribution can be transform to the normal distribution, which is symmetrical. Furthermore, variance is used to examine the dispersion of the fatigue life data. However, comparing the variances of two independent samples that follow BS distributions has not previously been reported. To accomplish this, we propose methods for providing the confidence interval for the ratio of variances of two independent BS distributions based on the generalized fiducial confidence interval (GFCI), a Bayesian credible interval (BCI), and the highest posterior density (HPD) intervals based on a prior distribution with partial information (HPD-PI) and a proper prior with known hyperparameters (HPD-KH). A Monte Carlo simulation study was carried out to examine the efficacies of the methods in terms of their coverage probabilities and average lengths. The simulation results indicate that the HPD-PI performed satisfactorily for all sample sizes investigated. To illustrate the efficacies of the proposed methods with real data, they were also applied to study the confidence interval for the ratio of the variances of two 6061-T6 aluminum coupon fatigue-life datasets.https://www.mdpi.com/2073-8994/14/7/1492Birnbaum–Saunders distributionconfidence intervalvariancefiducial inferenceBayesianfatigue life |
| spellingShingle | Wisunee Puggard Sa-Aat Niwitpong Suparat Niwitpong Confidence Intervals for Comparing the Variances of Two Independent Birnbaum–Saunders Distributions Symmetry Birnbaum–Saunders distribution confidence interval variance fiducial inference Bayesian fatigue life |
| title | Confidence Intervals for Comparing the Variances of Two Independent Birnbaum–Saunders Distributions |
| title_full | Confidence Intervals for Comparing the Variances of Two Independent Birnbaum–Saunders Distributions |
| title_fullStr | Confidence Intervals for Comparing the Variances of Two Independent Birnbaum–Saunders Distributions |
| title_full_unstemmed | Confidence Intervals for Comparing the Variances of Two Independent Birnbaum–Saunders Distributions |
| title_short | Confidence Intervals for Comparing the Variances of Two Independent Birnbaum–Saunders Distributions |
| title_sort | confidence intervals for comparing the variances of two independent birnbaum saunders distributions |
| topic | Birnbaum–Saunders distribution confidence interval variance fiducial inference Bayesian fatigue life |
| url | https://www.mdpi.com/2073-8994/14/7/1492 |
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