DOI QR코드

DOI QR Code

Modeling Circular Data with Uniformly Dispersed Noise

  • Yu, Hye-Kyung (Department of Information & Statistics, Chungbuk National University) ;
  • Jun, Kyoung-Ho (Office of Admission Management, Chungbuk National University) ;
  • Na, Jong-Hwa (Department of Information & Statistics, Chungbuk National University)
  • Received : 2012.05.22
  • Accepted : 2012.07.23
  • Published : 2012.08.31

Abstract

In this paper we developed a statistical model for circular data with noises. In this case, model fitting by single circular model has a lack-of-fit problem. To overcome this problem, we consider some mixture models that include circular uniform distribution and apply an EM algorithm to estimate the parameters. Both von Mises and Wrapped skew normal distributions are considered in this paper. Simulation studies are executed to assess the suggested EM algorithms. Finally, we applied the suggested method to fit 2008 EHFRS(Epidemic Hemorrhagic Fever with Renal Syndrome) data provided by the KCDC(Korea Centers for Disease Control and Prevention).

Keywords

References

  1. Batschelet, E. (1981). Circular Statistics in Biology, Academic Press, London.
  2. Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society, Series B, 39, 1-38.
  3. Fisher, N. I. (1993). Statistical Analysis of Circular Data, Cambridge University Press.
  4. Jammalamadaka, S. R. and SenGupta, A. (2001). Topics in Circular Statistics, World Scientific.
  5. Jang, Y. M., Yang, D. Y., Lee, J. Y. and Na, J. H. (2007). Modelling on multi-modal circular data using von Mises mixture distribution, The Korean Communications in Statistics, 14, 517-530. https://doi.org/10.5351/CKSS.2007.14.3.517
  6. Jennifer, A. M., Peter, J. H. and Ian, T. J. (2003). Fitting mixtures of von Mises distribution: A case study involving sudden infant death syndrome, Computational Statistics & Data Analysis, 41, 505-513. https://doi.org/10.1016/S0167-9473(02)00181-0
  7. Mardia, K. V. (1972). Statistics of Directional Data, Academic Press, New York.
  8. Na, J. H. and Jang, Y. M. (2010). Modeling on asymmetric circular data using wrapped skew-normal mixture, Journal of the Korean Data & Information Science Society, 21, 241-250.
  9. Na, J. H. and Jang, Y. M. (2011). Modeling on daily traffic volume of local state road using circular mixture distributions, The Korean Journal of Applied Statistics, 24, 547-557. https://doi.org/10.5351/KJAS.2011.24.3.547
  10. Pewsey, A. (2000). The wrapped skew-normal distribution on the circle, Communications in Statistics: Theory and Methods, 29, 2459-2472. https://doi.org/10.1080/03610920008832616
  11. Pewsey, A. (2004). Modelling asymmetrically distributed circular data using the wrapped skew-normal distribution, Environmental and Ecological Statistics, 13, 257-269.