Sequential Test for a Mixture of Finite Exponential Distribution
Testing the number of components in a finite mixture is considered one of the challenging problems. In this paper, exponential finite mixtures are used to determine the number of components in a finite mixture. A sequential testing procedure is adopted based on the likelihood ratio test (LRT) statis...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6625853 |
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| author | A.S. Al-Moisheer |
| author_facet | A.S. Al-Moisheer |
| author_sort | A.S. Al-Moisheer |
| collection | DOAJ |
| description | Testing the number of components in a finite mixture is considered one of the challenging problems. In this paper, exponential finite mixtures are used to determine the number of components in a finite mixture. A sequential testing procedure is adopted based on the likelihood ratio test (LRT) statistic. The distribution of the test statistic under the null hypothesis is obtained using a resampling technique based on B bootstrap samples. The quantiles of the distribution of the test statistic are evaluated from the B bootstrap samples. The performance of the test is examined through the empirical power and application on two real datasets. The proposed procedure is not only used for testing the number of components but also for estimating the optimal number of components in a finite exponential mixture distribution. The innovation of this paper is the sequential test, which tests the more general hypothesis of a finite exponential mixture of k components versus a mixture of k+1 components. The special case of testing an exponential mixture of one component versus two components is the one commonly used in the literature. |
| format | Article |
| id | doaj-art-691694dd266240348d6f658f4aa856a2 |
| institution | OA Journals |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-691694dd266240348d6f658f4aa856a22025-08-20T02:35:24ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66258536625853Sequential Test for a Mixture of Finite Exponential DistributionA.S. Al-Moisheer0Department of Mathematics, College of Science, Jouf University, P.O. Box 848, Sakaka 72351, Saudi ArabiaTesting the number of components in a finite mixture is considered one of the challenging problems. In this paper, exponential finite mixtures are used to determine the number of components in a finite mixture. A sequential testing procedure is adopted based on the likelihood ratio test (LRT) statistic. The distribution of the test statistic under the null hypothesis is obtained using a resampling technique based on B bootstrap samples. The quantiles of the distribution of the test statistic are evaluated from the B bootstrap samples. The performance of the test is examined through the empirical power and application on two real datasets. The proposed procedure is not only used for testing the number of components but also for estimating the optimal number of components in a finite exponential mixture distribution. The innovation of this paper is the sequential test, which tests the more general hypothesis of a finite exponential mixture of k components versus a mixture of k+1 components. The special case of testing an exponential mixture of one component versus two components is the one commonly used in the literature.http://dx.doi.org/10.1155/2021/6625853 |
| spellingShingle | A.S. Al-Moisheer Sequential Test for a Mixture of Finite Exponential Distribution Journal of Mathematics |
| title | Sequential Test for a Mixture of Finite Exponential Distribution |
| title_full | Sequential Test for a Mixture of Finite Exponential Distribution |
| title_fullStr | Sequential Test for a Mixture of Finite Exponential Distribution |
| title_full_unstemmed | Sequential Test for a Mixture of Finite Exponential Distribution |
| title_short | Sequential Test for a Mixture of Finite Exponential Distribution |
| title_sort | sequential test for a mixture of finite exponential distribution |
| url | http://dx.doi.org/10.1155/2021/6625853 |
| work_keys_str_mv | AT asalmoisheer sequentialtestforamixtureoffiniteexponentialdistribution |