On the power of Gini index-based goodness-of-fit test for the Inverse Gaussian distribution
The Inverse Gaussian distribution finds application in various fields, such as finance, survival analysis, psychology, engineering, physics, and quality control. Its capability to model skewed distributions and non-constant hazard rates makes it a valuable tool for understanding a wide range of phen...
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| Format: | Article |
| Language: | English |
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Shahid Bahonar University of Kerman
2025-01-01
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| Series: | Journal of Mahani Mathematical Research |
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| Online Access: | https://jmmrc.uk.ac.ir/article_4052_d9ac81fa92fe711e56adf8e4d7c55b60.pdf |
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| author | Hadi Alizadeh Noughabi Mohammad Shafaei Noughabi |
| author_facet | Hadi Alizadeh Noughabi Mohammad Shafaei Noughabi |
| author_sort | Hadi Alizadeh Noughabi |
| collection | DOAJ |
| description | The Inverse Gaussian distribution finds application in various fields, such as finance, survival analysis, psychology, engineering, physics, and quality control. Its capability to model skewed distributions and non-constant hazard rates makes it a valuable tool for understanding a wide range of phenomena. In this paper, we present a goodness-of-fit test specifically designed for the Inverse Gaussian distribution. Our test uses an estimate of the Gini index, a statistical measure of inequality. We provide comprehensive details on the exact and asymptotic distributions of the newly developed test statistic. To facilitate the application of the test, we estimate the unknown parameters of the Inverse Gaussian distribution using maximum likelihood estimators. Monte Carlo methods are utilized to determine the critical points and assess the actual sizes of the test. A power comparison study is conducted to evaluate the performance of existing tests. Comparing its powers with those of other tests, we demonstrate that the Gini index-based test performs favorably. Finally, we present a real data analysis for illustrative purposes. |
| format | Article |
| id | doaj-art-76165f4e36164a2c8e26261e31a385de |
| institution | Kabale University |
| issn | 2251-7952 2645-4505 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj-art-76165f4e36164a2c8e26261e31a385de2025-01-04T19:30:18ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052025-01-0114112210.22103/jmmr.2023.22215.15134052On the power of Gini index-based goodness-of-fit test for the Inverse Gaussian distributionHadi Alizadeh Noughabi0Mohammad Shafaei Noughabi1Department of Statistics, University of Birjand, Birjand, IranDepartment of Mathematics and Statistics, University of Gonabad, Gonabad, IranThe Inverse Gaussian distribution finds application in various fields, such as finance, survival analysis, psychology, engineering, physics, and quality control. Its capability to model skewed distributions and non-constant hazard rates makes it a valuable tool for understanding a wide range of phenomena. In this paper, we present a goodness-of-fit test specifically designed for the Inverse Gaussian distribution. Our test uses an estimate of the Gini index, a statistical measure of inequality. We provide comprehensive details on the exact and asymptotic distributions of the newly developed test statistic. To facilitate the application of the test, we estimate the unknown parameters of the Inverse Gaussian distribution using maximum likelihood estimators. Monte Carlo methods are utilized to determine the critical points and assess the actual sizes of the test. A power comparison study is conducted to evaluate the performance of existing tests. Comparing its powers with those of other tests, we demonstrate that the Gini index-based test performs favorably. Finally, we present a real data analysis for illustrative purposes.https://jmmrc.uk.ac.ir/article_4052_d9ac81fa92fe711e56adf8e4d7c55b60.pdfgini indextype-i errorcritical pointstest powermonte carlo simulation |
| spellingShingle | Hadi Alizadeh Noughabi Mohammad Shafaei Noughabi On the power of Gini index-based goodness-of-fit test for the Inverse Gaussian distribution Journal of Mahani Mathematical Research gini index type-i error critical points test power monte carlo simulation |
| title | On the power of Gini index-based goodness-of-fit test for the Inverse Gaussian distribution |
| title_full | On the power of Gini index-based goodness-of-fit test for the Inverse Gaussian distribution |
| title_fullStr | On the power of Gini index-based goodness-of-fit test for the Inverse Gaussian distribution |
| title_full_unstemmed | On the power of Gini index-based goodness-of-fit test for the Inverse Gaussian distribution |
| title_short | On the power of Gini index-based goodness-of-fit test for the Inverse Gaussian distribution |
| title_sort | on the power of gini index based goodness of fit test for the inverse gaussian distribution |
| topic | gini index type-i error critical points test power monte carlo simulation |
| url | https://jmmrc.uk.ac.ir/article_4052_d9ac81fa92fe711e56adf8e4d7c55b60.pdf |
| work_keys_str_mv | AT hadializadehnoughabi onthepowerofginiindexbasedgoodnessoffittestfortheinversegaussiandistribution AT mohammadshafaeinoughabi onthepowerofginiindexbasedgoodnessoffittestfortheinversegaussiandistribution |