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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:
QA Mathematics
Online Access: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
http://umpir.ump.edu.my/id/eprint/12731/
http://epg.science.cmu.ac.th/ejournal/dl.php?journal_id=5774
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spelling my.ump.umpir.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 http://epg.science.cmu.ac.th/ejournal/dl.php?journal_id=5774
institution Universiti Malaysia Pahang
building UMP Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Pahang
content_source UMP Institutional Repository
url_provider http://umpir.ump.edu.my/
language English
English
topic QA Mathematics
spellingShingle QA Mathematics
Siti Zanariah, Satari
Abdul Ghapor, Hussin
Yong Zulina, Zubairi
A New Efficient Approximation for Concentration Parameter of Circular Data
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.
format Article
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
title A New Efficient Approximation for Concentration Parameter of Circular Data
title_short 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_sort new efficient approximation for concentration parameter of circular data
publisher Chiangmai University
publishDate 2015
url 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
http://umpir.ump.edu.my/id/eprint/12731/
http://epg.science.cmu.ac.th/ejournal/dl.php?journal_id=5774
_version_ 1643666979087712256
score 13.211869

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