Information geometry and statistical manifold

Abstract A brief account of information geometry and the deep relationship between the differential geometry and the statistics is given [N.H. Abdel-All, International Conference on Differential Geometry and its Applications, Cairo University, 19–26 June, Egypt, 2001; Springer Lecture Notes in Statistics, vol. 28, 1985; Math. Syst. Theory 20 (1987) 53]. The parameter space of the random walk distribution (first passage time distributions of Brownian motion) using its Fisher's matrix is defined. The Riemannian and scalar curvatures in a parameter space are calculated. The differential equations of the geodesic are obtained and solved. The J -divergence, the geodesic distance and the relations between of them in that space are found in N.H. Abdel-All and elsewhere [Math. Comput. Model. 18 (8) (1993) 83; Bull. Calcutta Math. Soc. 37 (1945) 81].

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