On the approximation of the concentration parameter for von Mises distribution


  • 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




circular variable, concentration parameter, Monte Carlo, von Mises


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. 


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