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...

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Main Authors:	Nurkhairany Amyra Mokhtar, Yong Zulina Zubairi, Abdul Ghapor Hussin
Format:	Article
Language:	English
Published:	Penerbit Universiti Kebangsaan Malaysia 2017
Online Access:	http://journalarticle.ukm.my/11156/ http://journalarticle.ukm.my/11156/ http://journalarticle.ukm.my/11156/1/22%20Nurkhairany%20Amyra.pdf

id	ukm-11156
recordtype	eprints
spelling	ukm-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
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Kebangasaan Malaysia
building	UKM Institutional Repository
collection	Online Access
language	English
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.
format	Article
author	Nurkhairany Amyra Mokhtar, Yong Zulina Zubairi, Abdul Ghapor Hussin,
spellingShingle	Nurkhairany Amyra Mokhtar, Yong Zulina Zubairi, Abdul Ghapor Hussin, Estimation of concentration parameter for simultaneous circular functional relationship model assuming unequal error variance
author_facet	Nurkhairany Amyra Mokhtar, Yong Zulina Zubairi, Abdul Ghapor Hussin,
author_sort	Nurkhairany Amyra Mokhtar,
title	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_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_sort	estimation of concentration parameter for simultaneous circular functional relationship model assuming unequal error variance
publisher	Penerbit Universiti Kebangsaan Malaysia
publishDate	2017
url	http://journalarticle.ukm.my/11156/ http://journalarticle.ukm.my/11156/ http://journalarticle.ukm.my/11156/1/22%20Nurkhairany%20Amyra.pdf
first_indexed	2023-09-18T19:59:31Z
last_indexed	2023-09-18T19:59:31Z
_version_	1777406754410201088

Estimation of concentration parameter for simultaneous circular functional relationship model assuming unequal error variance

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