Exact Interval Inference for the Two-Parameter Rayleigh Distribution Based on the Upper Record Values
The maximum likelihood method is the most widely used estimation method. On the other hand, it can produce substantial bias, and an approximate confidence interval based on the maximum likelihood estimator cannot be valid when the sample size is small. Because the sizes of the record values are cons...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2016/8246390 |
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| _version_ | 1832551744522944512 |
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| author | Jung-In Seo Jae-Woo Jeon Suk-Bok Kang |
| author_facet | Jung-In Seo Jae-Woo Jeon Suk-Bok Kang |
| author_sort | Jung-In Seo |
| collection | DOAJ |
| description | The maximum likelihood method is the most widely used estimation method. On the other hand, it can produce substantial bias, and an approximate confidence interval based on the maximum likelihood estimator cannot be valid when the sample size is small. Because the sizes of the record values are considerably smaller than the original sequence observed in the majority of cases, a method appropriate for this situation is required for precise inference. This paper provides the exact confidence intervals for unknown parameters and exact predictive intervals for the future upper record values by providing some pivotal quantities in the two-parameter Rayleigh distribution based on the upper record values. Finally, the validity of the proposed inference methods was examined from Monte Carlo simulations and real data. |
| format | Article |
| id | doaj-art-85ecc15a78ad4bc0a1bb9b68a839e016 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-85ecc15a78ad4bc0a1bb9b68a839e0162025-02-03T06:00:42ZengWileyJournal of Probability and Statistics1687-952X1687-95382016-01-01201610.1155/2016/82463908246390Exact Interval Inference for the Two-Parameter Rayleigh Distribution Based on the Upper Record ValuesJung-In Seo0Jae-Woo Jeon1Suk-Bok Kang2Department of Statistics, Daejeon University, No. 62, Daehak-ro, Dong-gu, Republic of KoreaDepartment of Statistics, Yeungnam University, No. 280, Daehak-ro, Gyeongsan, Republic of KoreaDepartment of Statistics, Yeungnam University, No. 280, Daehak-ro, Gyeongsan, Republic of KoreaThe maximum likelihood method is the most widely used estimation method. On the other hand, it can produce substantial bias, and an approximate confidence interval based on the maximum likelihood estimator cannot be valid when the sample size is small. Because the sizes of the record values are considerably smaller than the original sequence observed in the majority of cases, a method appropriate for this situation is required for precise inference. This paper provides the exact confidence intervals for unknown parameters and exact predictive intervals for the future upper record values by providing some pivotal quantities in the two-parameter Rayleigh distribution based on the upper record values. Finally, the validity of the proposed inference methods was examined from Monte Carlo simulations and real data.http://dx.doi.org/10.1155/2016/8246390 |
| spellingShingle | Jung-In Seo Jae-Woo Jeon Suk-Bok Kang Exact Interval Inference for the Two-Parameter Rayleigh Distribution Based on the Upper Record Values Journal of Probability and Statistics |
| title | Exact Interval Inference for the Two-Parameter Rayleigh Distribution Based on the Upper Record Values |
| title_full | Exact Interval Inference for the Two-Parameter Rayleigh Distribution Based on the Upper Record Values |
| title_fullStr | Exact Interval Inference for the Two-Parameter Rayleigh Distribution Based on the Upper Record Values |
| title_full_unstemmed | Exact Interval Inference for the Two-Parameter Rayleigh Distribution Based on the Upper Record Values |
| title_short | Exact Interval Inference for the Two-Parameter Rayleigh Distribution Based on the Upper Record Values |
| title_sort | exact interval inference for the two parameter rayleigh distribution based on the upper record values |
| url | http://dx.doi.org/10.1155/2016/8246390 |
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