A New Efficient Approximation for Concentration Parameter of Circular Data

New and efficient approximations of the concentration parameter of circular data using two approaches are proposed in this paper. First, we consider the power series expansion of mean resultant length and the estimate of concentration parameter may be obtained by the roots of the polynomial funct...

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Main Authors: Siti Zanariah, Satari, Abdul Ghapor, Hussin, Yong Zulina, Zubairi
Format: Article
Language:English
English
Published: Chiangmai University 2015
Subjects:
Online Access:http://umpir.ump.edu.my/id/eprint/12731/
http://umpir.ump.edu.my/id/eprint/12731/1/2015%20Siti%20zanariah%20et%20al%20new%20efficient%20approximation%20for%20concentration%20parameter%20of%20circular%20data.pdf
http://umpir.ump.edu.my/id/eprint/12731/7/fist-2015-zanariah-new%20efficient%20approximation-full.pdf
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author Siti Zanariah, Satari
Abdul Ghapor, Hussin
Yong Zulina, Zubairi
author_facet Siti Zanariah, Satari
Abdul Ghapor, Hussin
Yong Zulina, Zubairi
author_sort Siti Zanariah, Satari
building UMP Institutional Repository
collection Online Access
description New and efficient approximations of the concentration parameter of circular data using two approaches are proposed in this paper. First, we consider the power series expansion of mean resultant length and the estimate of concentration parameter may be obtained by the roots of the polynomial function. Secondly, we consider the power series expansion of the reciprocal of a Bessel function in the log-likelihood function of the concentration parameter and the estimate of concentration parameter may be obtained by minimizing the negative value of the log-likelihood function. It is found that the new approximation solutions are more efficient compared to the other existing approximation solutions especially for large kappa.
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publisher Chiangmai University
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spelling ump-127312018-03-20T05:28:30Z http://umpir.ump.edu.my/id/eprint/12731/ A New Efficient Approximation for Concentration Parameter of Circular Data Siti Zanariah, Satari Abdul Ghapor, Hussin Yong Zulina, Zubairi QA Mathematics New and efficient approximations of the concentration parameter of circular data using two approaches are proposed in this paper. First, we consider the power series expansion of mean resultant length and the estimate of concentration parameter may be obtained by the roots of the polynomial function. Secondly, we consider the power series expansion of the reciprocal of a Bessel function in the log-likelihood function of the concentration parameter and the estimate of concentration parameter may be obtained by minimizing the negative value of the log-likelihood function. It is found that the new approximation solutions are more efficient compared to the other existing approximation solutions especially for large kappa. Chiangmai University 2015-04 Article PeerReviewed application/pdf en http://umpir.ump.edu.my/id/eprint/12731/1/2015%20Siti%20zanariah%20et%20al%20new%20efficient%20approximation%20for%20concentration%20parameter%20of%20circular%20data.pdf application/pdf en http://umpir.ump.edu.my/id/eprint/12731/7/fist-2015-zanariah-new%20efficient%20approximation-full.pdf Siti Zanariah, Satari and Abdul Ghapor, Hussin and Yong Zulina, Zubairi (2015) A New Efficient Approximation for Concentration Parameter of Circular Data. Chiang Mai Journal of Science, 42 (2). pp. 528-537. ISSN 0125-2526. (Published) http://epg.science.cmu.ac.th/ejournal/dl.php?journal_id=5774
spellingShingle QA Mathematics
Siti Zanariah, Satari
Abdul Ghapor, Hussin
Yong Zulina, Zubairi
A New Efficient Approximation for Concentration Parameter of Circular Data
title A New Efficient Approximation for Concentration Parameter of Circular Data
title_full A New Efficient Approximation for Concentration Parameter of Circular Data
title_fullStr A New Efficient Approximation for Concentration Parameter of Circular Data
title_full_unstemmed A New Efficient Approximation for Concentration Parameter of Circular Data
title_short A New Efficient Approximation for Concentration Parameter of Circular Data
title_sort new efficient approximation for concentration parameter of circular data
topic QA Mathematics
url http://umpir.ump.edu.my/id/eprint/12731/
http://umpir.ump.edu.my/id/eprint/12731/
http://umpir.ump.edu.my/id/eprint/12731/1/2015%20Siti%20zanariah%20et%20al%20new%20efficient%20approximation%20for%20concentration%20parameter%20of%20circular%20data.pdf
http://umpir.ump.edu.my/id/eprint/12731/7/fist-2015-zanariah-new%20efficient%20approximation-full.pdf