A Note on Finding Geodesic Equation of Two Parameters Gamma Distribution

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References

[1] Struik, D.J. (1961) Lectures on Classical Differential Geometry. 2nd Edition, Dover Publications, Inc., New York.

[2] Lauritzen, S.L. (1987) Chapter 4: Statistical Manifolds. Differential Geometry in Statistical Inference. Vol. 10, Institute of Mathematical Statistics, Lecture Notes Monograph Series, Hayward, 163-216.

[3] Rao, C.R. (1945) Information and the Accuracy Attainable in the Estimation of Statistical Parameters. Bulletin of Calcutta Mathematical Society, 37, 81-91.

[4] Mitchell, A.F.S. (1988) Statistical Manifolds of Univariate Elliptic Distributions. International Statistical Review, 56, 1-16.

http://dx.doi.org/10.2307/1403358

[5] Oller, J.M. (1987) Information Metric for Extreme Value and Logistic Probability Distributions. Sankhya A, 49, 17-23.

[6] Chen, W.W.S. (1998) Curvature: Gaussian or Riemann. International Conference (IISA), McMaster University, Hamilton, October.

[7] Chen, W.W.S. and Kotz, S. (2013) The Riemannian Structure of the Three-Parameter Gamma Distribution. Applied Mathematics, 4, 514-522.

[8] Darboux, G. (1889-1997) Lecons sur la theorie generale des surfaces. Gauthier-Villars, Paris.

[9] Amari, S.I. (1982) Differential Geometry of Curved Exponential Families Curvature and Information Loss. Annals of Statistics, 10, 357-385.

http://dx.doi.org/10.1214/aos/1176345779

[10] Gray, A. (1993) Modern Differential Geometry of Curves and Surfaces. CRC Press, Inc., Boca Raton.