On the approximation of the concentration parameter for von Mises distribution

Nor Hafizah Moslim, Yong Zulina Zubairi, Abdul Ghapor Hussin, Siti Fatimah Hassan, Rossita Mohamad Yunus

Abstract


The von Mises distribution is the ‘natural’ analogue on the circle of the Normal distribution on the real line and is widely used to describe circular variables. The distribution has two parameters, namely mean direction,  and concentration parameter, κ. Solutions to the parameters, however, cannot be derived in the closed form. Noting the relationship of the κ to the size of sample, we examine the asymptotic normal behavior of the parameter. The simulation study is carried out and Kolmogorov-Smirnov test is used to test the goodness of fit for three level of significance values. The study suggests that as sample size and concentration parameter increase, the percentage of samples follow the normality assumption increase. 


Keywords


circular variable; concentration parameter; Monte Carlo, von Mises

Full Text:

PDF

References


Jammalamadaka, S. R. and Sengupta, A. 2001. Topics in Circular Statistics. London: World Scientific. Mardia, K. V. 1972. Statistics of Directional Data. London: Academic Press.

Mardia, K. V. and Jupp, P. E. 2000. Directional Statistics. England: John Wiley & Sons Ltd.

Abuzaid, A. H., Hussin, A. G., Rambli, A. and Mohamed, I. 2012. Statistics for a new test of discordance in circular data. Communications in Statistics – Simulation and Computation. 41, 1882-1890.

Amos D. E. 1974. Computation of modified bessel functions and their ratios. Mathematics of Computation. 28(125), 239-251. Dobson A. J. 1978. Simple approximations for the Von Mises concentration statistic. Journal of the Royal Statistical Society, Series C (Applied Statistics). 27(3), 345-347.

Fisher N. 1. 1993. Statistical Analysis of Circular Data. Canberra: Cambridge University Press.




DOI: https://doi.org/10.11113/mjfas.v13n4-1.807

Refbacks

  • There are currently no refbacks.


Copyright (c) 2017 Nor Hafizah Moslim, Yong Zulina Zubairi, Abdul Ghapor Hussin, Siti Fatimah Hassan, Rossita Mohamad Yunus

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.


Copyright © 2005-2019 Penerbit UTM Press, Universiti Teknologi Malaysia. Disclaimer: This website has been updated to the best of our knowledge to be accurate. However, Universiti Teknologi Malaysia shall not be liable for any loss or damage caused by the usage of any information obtained from this website.