Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
권호 표지

A note on the geometric structure of the t-distribution

  • Cho, Bong-Sik (Division of Mathematics and Information Statistics, Wonkwang University) ;
  • Jung, Sun-Young (College of Engineering, Hanyang University)
  • Received : 2010.03.24
  • Accepted : 2010.05.23
  • Published : 2010.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

The Fisher information matrix plays a significant role in statistical inference in connection with estimation and properties of variance of estimators. In this paper, the parameter space of the t-distribution using its Fisher's matrix is de ned. The ${\alpha}$-scalar curvatures to parameter space are calculated.

Keywords

References

  1. Adbel-All, N. H., Abd-Ellah, H. N. and Moustafa, H. M. (2003). Information geometry and statistical manifold. Chaos, Solitons and Fractals, 15, 161-172. https://doi.org/10.1016/S0960-0779(02)00142-X
  2. Amari, S. (1982). Differential geometry of curved exponential families-curvatures and information loss. Annals of Statistics, 10, 357-385. https://doi.org/10.1214/aos/1176345779
  3. Amari, S. (1985). Differential geometrical methods in statistics. Springer Lecture Notes in Statistics, 28.
  4. Arwini, K. A. and Dodson, C. T. J. (2007). Alpha-geometry of the Weibull manifold, Second Basic Sciences Conference, Al-Fatah University, Tripoli, Libya 4-8.
  5. Cho, B. S. and Baek, H. Y. (2006). Geometric properties of t-distribution. Honam Mathematical Journal, 28, 433-438.
  6. Efron, B. (1975). Defining the curvature of a statistical problem. Annals of Statistics, 3, 1109-1242. https://doi.org/10.1214/aos/1176343243
  7. Kass, R. E. and Vos, P. W. (1997). Geometrical foundations of asymptotic inference, John Wiley & Sons, Inc.
  8. Kass, R. E. (1989). The geometry of asymptotic inference. Statistical Science, 4, 188- 219. https://doi.org/10.1214/ss/1177012480
  9. Rao, C. R. (1945). Information and the accuracy attainable in estimation of statistical parameters. Bulletin of the Calcutta Mathematical Society, 37, 81-91.
  10. Wagenaar, D. A. (1998). Information geometry for neural networks, Term paper for reading course with A. C. C. Coolen, King's College, London.