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A Note on Finding Geodesic Equation of Two Parameters Gamma Distribution

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Author(s)   
Engineers commonly use the gamma distribution to describe the life span or metal fatigue of a manufactured item. In this paper, we focus on finding a geodesic equation of the two parameters gamma distribution. To find this equation, we applied both the well-known Darboux Theorem and a pair of differential equations taken from Struik [1]. The solution proposed in this note could be used as a general solution of the geodesic equation of gamma distribution. It would be interesting if we compare our results with Lauritzen’s [2].
Cite this paper
Chen, W. (2014) A Note on Finding Geodesic Equation of Two Parameters Gamma Distribution. Applied Mathematics, 5, 3511-3517. doi: 10.4236/am.2014.521328. 
 

[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.                                 eww141225lx
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