A New Efficient Approximation for Concentration Parameter of Circular Data
Siti Zabariah Satari, Abdul Ghapor Hussin and Yang Zulina Zubairi* Author for corresponding; e-mail address: zanariah@ump.edu.my
Volume: Vol.42 No.2 (APRIL 2015)
Research Article
DOI:
Received: 21 Febuary 2012, Revised: -, Accepted: 29 May 2013, Published: -
Citation: Satari S.Z., Hussin A.G. and Zubairi Y.Z., A New Efficient Approximation for Concentration Parameter of Circular Data, Chiang Mai Journal of Science, 2015; 42(2): 528-537.
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 .