DOI QR코드

DOI QR Code

Hidden truncation circular normal distribution

  • Kim, Sung-Su (Department of English Education, Keimyung University) ;
  • Sengupta, Ashis (Applied Statistics Unit, Indian Statistical Institute)
  • Received : 2012.05.14
  • Accepted : 2012.06.04
  • Published : 2012.07.31

Abstract

Many circular distributions are known to be not only asymmetric but also bimodal. Hidden truncation method of generating asymmetric distribution is applied to a bivariate circular distribution to generate an asymmetric circular distribution. While many other existing asymmetric circular distributions can only model an asymmetric data, this new circular model has great flexibility in terms of asymmetry and bi-modality. Some properties of the new model, such as the trigonometric moment generating function, and asymptotic inference about the truncation parameter are presented. Simulation and real data examples are provided at the end to demonstrate the utility of the novel distribution.

References

  1. Arnold, B. and Beaver, R. (2000). Hidden truncation models. Sankhya, 62, 23-35.
  2. Azzalini, A. (1986). A class of distributions which includes the normal ones. Scandinavian Journal of Statististics, 12, 171-178.
  3. Batschelet, E. (1981). Circular statistics in biology, Academic Press, Inc., New York.
  4. Casella, G. and Berger, R. (2001). Statistical inference, Duxbury Advanced Series, Pacific Grove, CA.
  5. Chernoff, H. (1954). On the distribution of the likelihood ratio. Annals of Mathematical Statistics, 25, 573-578. https://doi.org/10.1214/aoms/1177728725
  6. Fisher, N. I. (1993). Statistical analysis of circular data, Cambridge University Press, Cambridge.
  7. Fernandez-Duran Fernadez-Duran, J. (2004) Circular distributions based on nonnegative trigonometric sums. Biometrics, 60, 499-503. https://doi.org/10.1111/j.0006-341X.2004.00195.x
  8. Gatto, R. and Jammalamadaka, S. (2007). The generalized von Mises distribution. Statistical Methodology, 4, 341-353. https://doi.org/10.1016/j.stamet.2006.11.003
  9. Jammalamadaka, S. and Kozubowski, T. (2004). New families of wrapped distributions for modeling skew circular data. Communication in Statistics Theory and Methods, 33, 2059-2074. https://doi.org/10.1081/STA-200026570
  10. Jammalamadaka, S. and SenGupta, A. (2001). Topics in circular statistics, Scientific Publishing CO., New York.
  11. Kim, S. (2011). Exponential family of circular distributions. Journal of the Korean Data & Information Society, 22, 298-303.
  12. Kim, S. (2011). Circular regression using geodesic lines. Journal of the Korean Data & Information Society, 22, 961-966.
  13. Royden, H. L. (1988). Real analysis, Prentice-Hall, Inc, New Jersey.
  14. Self, S. G. and Liang, K. Y. (1987). Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. Journal of the American Statistical Association, 82, 605-610. https://doi.org/10.1080/01621459.1987.10478472
  15. SenGupta, A. and Ugwuowo, F. (2006). Asymmetric circular-linear multivariate regression models with applications to environmental data. Journal of Environmental Statistics, 13, 299-309. https://doi.org/10.1007/s10651-005-0013-1
  16. Umbach, D. and Jammalamadaka, S. (2009). Building asymmetry into circular distribution. Statistics and Probability Letters, 79, 659-663. https://doi.org/10.1016/j.spl.2008.10.022