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α-SCALAR CURVATURE OF THE t-MANIFOLD
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  • Journal title : Honam Mathematical Journal
  • Volume 33, Issue 4,  2011, pp.487-493
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2011.33.4.487
 Title & Authors
α-SCALAR CURVATURE OF THE t-MANIFOLD
Cho, Bong-Sik; Jung, Sun-Young;
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 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, we define the parameter space of the t-manifold using its Fisher`s matrix and characterize the t-manifold from the viewpoint of information geometry. The -scalar curvatures to the t-manifold are calculated.
 Keywords
-connection;-scalar curvature;
 Language
English
 Cited by
 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. crossref(new window)

2.
Amari, S. (1982). Differential geometry of curved exponential families-curvatures and information loss. Ann. Statist. 10.

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. Annual. Statis- tics. 3, 1109-1242. crossref(new window)

7.
Kass, R. E. and Vos, P. W. (1997). Geometrical foundations of asymptotic infer ence, John Wiley and Sons, Inc.

8.
Kass, R. E. (1989). The geometry of asymptotic inference, Statistical Science, 4, 188-219. crossref(new window)

9.
Murray, M. K. and Rice, J. W. (1993). Differential geometry and Statistics, Chapman and Hall, New York.

10.
Rao, C. R. (1945). Information and the accuracy attainable in estimation of statistical parameters, Bull. Calcutta Math. Soc, 37, 81-91.