On the approximation of the concentration parameter for von Mises distribution

Authors

  • Nor Hafizah Moslim Faculty of Industrial Sciences & Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Pahang Centre for Foundation Studies in Science, University of Malaya, 50603 Kuala Lumpur
  • Yong Zulina Zubairi Centre for Foundation Studies in Science, University of Malaya, 50603 Kuala Lumpur
  • Abdul Ghapor Hussin Faculty of Defence Sciences and Technology, National Defence University of Malaysia, Kem Sungai Besi, 57000 Kuala Lumpur
  • Siti Fatimah Hassan Centre for Foundation Studies in Science, University of Malaya, 50603 Kuala Lumpur
  • Rossita Mohamad Yunus Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur

DOI:

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

Keywords:

circular variable, concentration parameter, Monte Carlo, von Mises

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. 

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.

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Published

05-12-2017

Issue

Special Issue on Some Advances in Industrial and Applied Mathematics (ISMI 2017)

Section

Article