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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Bibliographic Details
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/
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
Description
Summary: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.