Estimation of concentration parameter for simultaneous circular functional relationship model assuming unequal error variance
In this study, we propose the estimation of the concentration parameter for simultaneous circular functional relationship model. In this case, the variances of the error term are not necessarily equal and the ratio of the concentration parameter λ = is not necessarily 1. The modified Bessel function...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Penerbit Universiti Kebangsaan Malaysia
2017
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| Online Access: | http://journalarticle.ukm.my/11156/ http://journalarticle.ukm.my/11156/1/22%20Nurkhairany%20Amyra.pdf |
| _version_ | 1848812633537380352 |
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| author | Nurkhairany Amyra Mokhtar, Yong Zulina Zubairi, Abdul Ghapor Hussin, |
| author_facet | Nurkhairany Amyra Mokhtar, Yong Zulina Zubairi, Abdul Ghapor Hussin, |
| author_sort | Nurkhairany Amyra Mokhtar, |
| building | UKM Institutional Repository |
| collection | Online Access |
| description | In this study, we propose the estimation of the concentration parameter for simultaneous circular functional relationship model. In this case, the variances of the error term are not necessarily equal and the ratio of the concentration parameter λ = is not necessarily 1. The modified Bessel function was expended by using the asymptotic power series and it became a cubic equation of κ. From the cubic equation of κ, the roots were obtained by using the polyroot function in SPlus software. Simulation study was done to study the mean, estimated bias, absolute relative estimated bias, estimated standard error and estimated root mean square error of the estimation of the concentration parameter. From the simulation study, large concentration parameter and sample size show that the estimated concentration parameter has smaller bias. Also, an illustration to a real wind and wave data set is given to show its practical applicability. |
| first_indexed | 2025-11-15T00:05:24Z |
| format | Article |
| id | oai:generic.eprints.org:11156 |
| institution | Universiti Kebangasaan Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T00:05:24Z |
| publishDate | 2017 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | oai:generic.eprints.org:111562017-12-23T02:33:32Z http://journalarticle.ukm.my/11156/ Estimation of concentration parameter for simultaneous circular functional relationship model assuming unequal error variance Nurkhairany Amyra Mokhtar, Yong Zulina Zubairi, Abdul Ghapor Hussin, In this study, we propose the estimation of the concentration parameter for simultaneous circular functional relationship model. In this case, the variances of the error term are not necessarily equal and the ratio of the concentration parameter λ = is not necessarily 1. The modified Bessel function was expended by using the asymptotic power series and it became a cubic equation of κ. From the cubic equation of κ, the roots were obtained by using the polyroot function in SPlus software. Simulation study was done to study the mean, estimated bias, absolute relative estimated bias, estimated standard error and estimated root mean square error of the estimation of the concentration parameter. From the simulation study, large concentration parameter and sample size show that the estimated concentration parameter has smaller bias. Also, an illustration to a real wind and wave data set is given to show its practical applicability. Penerbit Universiti Kebangsaan Malaysia 2017-08 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/11156/1/22%20Nurkhairany%20Amyra.pdf Nurkhairany Amyra Mokhtar, and Yong Zulina Zubairi, and Abdul Ghapor Hussin, (2017) Estimation of concentration parameter for simultaneous circular functional relationship model assuming unequal error variance. Sains Malaysiana, 46 (8). pp. 1347-1353. ISSN 0126-6039 http://www.ukm.my/jsm/malay_journals/jilid46bil8_2017/KandunganJilid46Bil8_2017.html |
| spellingShingle | Nurkhairany Amyra Mokhtar, Yong Zulina Zubairi, Abdul Ghapor Hussin, Estimation of concentration parameter for simultaneous circular functional relationship model assuming unequal error variance |
| title | Estimation of concentration parameter for simultaneous circular functional relationship model assuming unequal error variance |
| title_full | Estimation of concentration parameter for simultaneous circular functional relationship model assuming unequal error variance |
| title_fullStr | Estimation of concentration parameter for simultaneous circular functional relationship model assuming unequal error variance |
| title_full_unstemmed | Estimation of concentration parameter for simultaneous circular functional relationship model assuming unequal error variance |
| title_short | Estimation of concentration parameter for simultaneous circular functional relationship model assuming unequal error variance |
| title_sort | estimation of concentration parameter for simultaneous circular functional relationship model assuming unequal error variance |
| url | http://journalarticle.ukm.my/11156/ http://journalarticle.ukm.my/11156/ http://journalarticle.ukm.my/11156/1/22%20Nurkhairany%20Amyra.pdf |