Sequential Probabilistic Ratio Test for the Scale Parameter of the P-Norm Distribution
We consider a series of independent observations from a P-norm distribution with the position parameter μ and the scale parameter σ. We test the simple hypothesis H0:σ=σ1 versus H1: σ=σ2. Firstly, we give the stop rule and decision rule of sequential probabilistic ratio test (SPRT). Secondly, we pro...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2021/9922435 |
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| _version_ | 1850222786698543104 |
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| author | Huan Ren Hongchang Hu Zhen Zeng |
| author_facet | Huan Ren Hongchang Hu Zhen Zeng |
| author_sort | Huan Ren |
| collection | DOAJ |
| description | We consider a series of independent observations from a P-norm distribution with the position parameter μ and the scale parameter σ. We test the simple hypothesis H0:σ=σ1 versus H1: σ=σ2. Firstly, we give the stop rule and decision rule of sequential probabilistic ratio test (SPRT). Secondly, we prove the existence of hσ which needs to satisfy the specific situation in SPRT method, and the approximate formula of the mean sample function is derived. Finally, a simulation example is given. The simulation shows that the ratio of sample size required by SPRT and the classic Neyman–Pearson N−P test is about 50.92% at most,38.30% at least. |
| format | Article |
| id | doaj-art-6e9746ff9c664be7b991602eebc6a5f2 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-6e9746ff9c664be7b991602eebc6a5f22025-08-20T02:06:12ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2021-01-01202110.1155/2021/99224359922435Sequential Probabilistic Ratio Test for the Scale Parameter of the P-Norm DistributionHuan Ren0Hongchang Hu1Zhen Zeng2College of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, ChinaCollege of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, ChinaSchool of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, ChinaWe consider a series of independent observations from a P-norm distribution with the position parameter μ and the scale parameter σ. We test the simple hypothesis H0:σ=σ1 versus H1: σ=σ2. Firstly, we give the stop rule and decision rule of sequential probabilistic ratio test (SPRT). Secondly, we prove the existence of hσ which needs to satisfy the specific situation in SPRT method, and the approximate formula of the mean sample function is derived. Finally, a simulation example is given. The simulation shows that the ratio of sample size required by SPRT and the classic Neyman–Pearson N−P test is about 50.92% at most,38.30% at least.http://dx.doi.org/10.1155/2021/9922435 |
| spellingShingle | Huan Ren Hongchang Hu Zhen Zeng Sequential Probabilistic Ratio Test for the Scale Parameter of the P-Norm Distribution Discrete Dynamics in Nature and Society |
| title | Sequential Probabilistic Ratio Test for the Scale Parameter of the P-Norm Distribution |
| title_full | Sequential Probabilistic Ratio Test for the Scale Parameter of the P-Norm Distribution |
| title_fullStr | Sequential Probabilistic Ratio Test for the Scale Parameter of the P-Norm Distribution |
| title_full_unstemmed | Sequential Probabilistic Ratio Test for the Scale Parameter of the P-Norm Distribution |
| title_short | Sequential Probabilistic Ratio Test for the Scale Parameter of the P-Norm Distribution |
| title_sort | sequential probabilistic ratio test for the scale parameter of the p norm distribution |
| url | http://dx.doi.org/10.1155/2021/9922435 |
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