Browse > Article

Modeling sharply peaked asymmetric multi-modal circular data using wrapped Laplace mixture  

Na, Jong-Hwa (Department of Information and Statistics, Chungbuk National University)
Jang, Young-Mi (Korea Health and Welfare Information Service)
Publication Information
Journal of the Korean Data and Information Science Society / v.21, no.5, 2010 , pp. 863-871 More about this Journal
Abstract
Until now, many studies related circular data are carried out, but the focuses are mainly on mildly peaked symmetric or asymmetric cases. In this paper we studied a modeling process for sharply peaked asymmetric circular data. By using wrapped Laplace, which was firstly introduced by Jammalamadaka and Kozbowski (2003), and its mixture distributions, we considered the model fitting problem of multi-modal circular data as well as unimodal one. In particular we suggested EM algorithm to find ML estimates of the mixture of wrapped Laplace distributions. Simulation results showed that the suggested EM algorithm is very accurate and useful.
Keywords
Circular data; mixture model; wrapped Laplace;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 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.   과학기술학회마을   DOI   ScienceOn
2 Dempster, Laird and Rubin (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society B, 39, 1-38.
3 Jammalamadaka, S. R. and Kozubowski, T. J. (2003). A new family of circular models: The wrapped Laplace distributions. Advances and Application in Statistics, 3, 77-103.
4 Jammalamadaka, S. R. and SenGupta, A. (2001). Topics in circular statistics, World Scientific.
5 Batschelet, E. (1981). Circular statistics in biology, Academic Press, London.
6 Tanner, M. A. (1996). Tools for statistical inference, Springer.
7 Papakonstantinou, V. (1979). Bietrge zur zirkulren statistik , PhD Dissertation, University of Zurich, Switzerland.
8 Pewsey, A. (2000). The wrapped skew-normal distribution on the circle. Communications in Statistics:Theory and Methods, 29, 2459-2472.   DOI   ScienceOn
9 Pewsey, A. (2006). Modelling asymmetrically distributed circular data using the wrapped skew-normal distribution. Environmental and Ecological Statistics, 13, 257-269.   DOI   ScienceOn
10 Titterington, D. M., Smith, A. F. M., and Makov, U. E. (1985). Statistical analysis of finite mixture distributions, Wiley, Chichester.
11 Mardia, K. V. and Jupp, P. E. (1999). Directional statistics, Wiley.
12 Na, J. H. and Jang, Y. M. (2010b). Modeling on daily traffic volume of local state road using circular mixture distributions. Unpublished Manuscript.
13 Nelder, J. A. and Mead, R. (1965). A simplex method for function minimization. Computer Journal, 7, 308-313.   DOI
14 McLachlan, G. J. and Krishnan, T. (1997). The EM algorithm and extensions, Wiley.
15 Mooney, J. A., Helms, P. J. and Jolliffe, I. T. (2003). Fitting mixtures of von Mises distributions: A case study involving sudden infant death syndrome. Computational Statistics and Data Analysis, 41, 505-513.   DOI   ScienceOn
16 Na, J. H. and Jang, Y. M. (2010a). Modeling on asymmetric circular data using wrapped skew-normal mixture. Journal of the Korean Data & Information Science Society, 21, 241-250.   과학기술학회마을
17 Mardia, K. V. (1972). Statistics of directional data, Academic Press, New York.