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A New Efficient Approximation for Concentration Parameter of Circular Data

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

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Abstract

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.

Item Type: Article
Uncontrolled Keywords: Mean resultant length, concentration parameter, modified Bessel function, von Mises distribution, maximum likelihood estimator
Subjects: Q Science > QA Mathematics
Faculty/Division: Faculty of Industrial Sciences And Technology
Depositing User: Ms. Siti Zanariah Satari
Date Deposited: 07 Apr 2016 06:08
Last Modified: 20 Mar 2018 05:28
URI: http://umpir.ump.edu.my/id/eprint/12731
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