A General Approach for Obtaining Wrapped Circular Distributions via Mixtures
- 113 Downloads
We show that the operations of mixing and wrapping linear distributions around a unit circle commute, and can produce a wide variety of circular models. In particular, we show that many wrapped circular models studied in the literature can be obtained as scale mixtures of just the wrapped Gaussian and the wrapped exponential distributions, and inherit many properties from these two basic models. We also point out how this general approach can produce flexible asymmetric circular models, the need for which has been noted by many authors.
Keywords and phrasesCircular data Wrapped distributions Mixtures Wrapped normal Wrapped exponential Scale mixtures
AMS (2010) Subject ClassificationPrimary 62H11 Secondary 60E05, 62E10
Unable to display preview. Download preview PDF.
- Ayebo, A. and Kozubowski, T. J. (2003). An asymmetric generalization of Gaussian and Laplace laws. J. Probab. Statist. Sci. 1, 187–210.Google Scholar
- Ghosh, M., Choi, K. P. and Li, J. (2010) A commentary on the logistic distribution. In The Legacy of Alladi Ramakrishnan in the Mathematical Sciences, (K. Alladi, J. R. Klauder and C. R. Rao, eds.). pp. 351–357, Springer, New York.Google Scholar
- Gleser, L. J. (1987). The gamma distribution as a mixture of exponential distributions. Technical Report No 87-28. Department of Statistics, Purdue University.Google Scholar
- Jammalamadaka, S. and Kozubowski, T. J. (2001). A wrapped exponential circular model. Proc. Andhra Pradesh Academy Sci. 5, 43–56.Google Scholar
- Johnson, N. L., Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions, 1, 2nd Edn. Wiley, New York.Google Scholar
- Johnson, N. L., Kotz S. and Balakrishnan, N. (1995). Continuous Univariate Distributions, 2, 2nd Edn. Wiley, New York.Google Scholar
- Kato, S. and Shimizu, K. (2004). A further study of t-distributions on spheres. Technical Report School of Fundamental Science and Technology. Keio University, Yokohama.Google Scholar
- Steutel, F. W. and van Harn, K. (2004). Infinite Divisibility of Probability Distributions on the Real Line. Marcel Dekker, New York.Google Scholar