A New Efficient Approximation for Concentration Parameter of Circular Data

• Main Authors: Siti Zabariah Satari", Abdul Ghapor Hussin, Yang Zulina Zubairi
• Language: English
• Published: Science Faculty of Chiang Mai University 2019
• Subjects: Mean resultant length; concentration parameter; modified Bessel function; von Mises distribution; maximum likelihood estimator
• Online Access: http://it.science.cmu.ac.th/ejournal/dl.php?journal_id=5774; http://cmuir.cmu.ac.th/jspui/handle/6653943832/66824
• Institution: Chiang Mai University

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 .