Saddlepoint approximation for the p-values of some distribution-free tests
This article discusses the saddlepoint approximation for the p-values of some distribution-free tests, a signed rank test for bivariate location problems and a dispersion test for scale problems. The statistics of the two considered tests are constructed based on the ratio of two variables. The accu...
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| Format: | Article |
| Language: | English |
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AIMS Press
2025-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025121 |
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| author | Abd El-Raheem M. Abd El-Raheem Mona Hosny |
| author_facet | Abd El-Raheem M. Abd El-Raheem Mona Hosny |
| author_sort | Abd El-Raheem M. Abd El-Raheem |
| collection | DOAJ |
| description | This article discusses the saddlepoint approximation for the p-values of some distribution-free tests, a signed rank test for bivariate location problems and a dispersion test for scale problems. The statistics of the two considered tests are constructed based on the ratio of two variables. The accuracy of the saddlepoint approximation is compared to traditional asymptotic normal approximation by applying numerical comparisons. Furthermore, the proposed approximations are illustrated by analyzing numerical examples. The results of numerical comparisons indicate that the approximation error resulting from the proposed method is much lower than the traditional method, which is evidence of the superiority of the proposed approximation method over the traditional method. Accordingly, we can say that the saddlepoint approximation method can be a competitive alternative to the traditional method. |
| format | Article |
| id | doaj-art-825d76fa48554a5f8fc1ad8682320d64 |
| institution | DOAJ |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-825d76fa48554a5f8fc1ad8682320d642025-08-20T03:17:09ZengAIMS PressAIMS Mathematics2473-69882025-02-011022602261810.3934/math.2025121Saddlepoint approximation for the p-values of some distribution-free testsAbd El-Raheem M. Abd El-Raheem0Mona Hosny1Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11566, EgyptDepartment of Mathematics, College of Science, King Khalid University, Abha, 61413, Saudi ArabiaThis article discusses the saddlepoint approximation for the p-values of some distribution-free tests, a signed rank test for bivariate location problems and a dispersion test for scale problems. The statistics of the two considered tests are constructed based on the ratio of two variables. The accuracy of the saddlepoint approximation is compared to traditional asymptotic normal approximation by applying numerical comparisons. Furthermore, the proposed approximations are illustrated by analyzing numerical examples. The results of numerical comparisons indicate that the approximation error resulting from the proposed method is much lower than the traditional method, which is evidence of the superiority of the proposed approximation method over the traditional method. Accordingly, we can say that the saddlepoint approximation method can be a competitive alternative to the traditional method.https://www.aimspress.com/article/doi/10.3934/math.2025121bivariate signed rank testslocation problemssaddlepoint approximationsscale problems |
| spellingShingle | Abd El-Raheem M. Abd El-Raheem Mona Hosny Saddlepoint approximation for the p-values of some distribution-free tests AIMS Mathematics bivariate signed rank tests location problems saddlepoint approximations scale problems |
| title | Saddlepoint approximation for the p-values of some distribution-free tests |
| title_full | Saddlepoint approximation for the p-values of some distribution-free tests |
| title_fullStr | Saddlepoint approximation for the p-values of some distribution-free tests |
| title_full_unstemmed | Saddlepoint approximation for the p-values of some distribution-free tests |
| title_short | Saddlepoint approximation for the p-values of some distribution-free tests |
| title_sort | saddlepoint approximation for the p values of some distribution free tests |
| topic | bivariate signed rank tests location problems saddlepoint approximations scale problems |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025121 |
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