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: | , , |
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| Format: | Article |
| Language: | English English |
| Published: |
Chiangmai University
2015
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| Subjects: | |
| 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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| 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. |
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