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A NOTE ON THE GEOMETRICAL PROPERTIES OF THE NORMAL DISTRIBUTION

  • Cho, Bong-Sik (Division of Mathematics and Information Statistics Research institute for basic sciences Wonkwang University)
  • Received : 2007.02.07
  • Accepted : 2007.03.28
  • Published : 2007.03.25

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 normal distribution using its Fisher's matrix is defined. The Riemannian curvature and J-divergence to parameter space are calculated.

Keywords

References

  1. Abdel, N. H., Mahmoud, M. A. W., Moustafa, H. M. Information geometry and statistical manifold, Chaos, Solitons and Fractals 15 (2003) 161-172. https://doi.org/10.1016/S0960-0779(02)00142-X
  2. Abdel, N. H., Mahmoud, M. A. W., Abd-EUah, H. N. Geometrical properties of Pareto distribution, Appl. Math, and Computation 145 (2003) 321-339. https://doi.org/10.1016/S0096-3003(02)00490-3
  3. Amari, S. Differential geometrical methods in statistics, Lecture notes in statis­tics, 28, Springer Verlag, Heidelberg (1986).
  4. Amari, S. and Nagaoka, H. Methods of information geometry, 191, A. M. S. (1993).
  5. Chen, W. W. S. On computing Gaussian curvature of some well known distributions, A. S. A. : section on Bayesian statistical science (1999), 129-134.
  6. Costa, S. I. R. and Santos, S. A. and Strapasson, J. E. Fisher information matrix and hyperbolic geometry, Information Theory Workshop, 2005 IEEE (2005), 28-30. https://doi.org/10.1109/ITW.2005.1531851
  7. Edwards, R. D. International distributions of the age at death and mortality convergence, Population association of America 2004 Annual Meeting Program, Boston, Massachusetts, April 1-3 (2004).
  8. Rao, C. R. Information and the accuracy attainable in the estimation of statistical parameters, Bull. Calcutta Math. Soc. 37 (1945) 81-91.