Abstract
we analyze the geometrical structures of statistical manifoldSconsisting of all the wrapped Cauchy distributions. We prove thatSis a simply connected manifold with constant negative curvatureK=-2. However, it is not isometric to the hyperbolic space becauseSis noncomplete. In fact,Sis approved to be a cohomogeneity one manifold. Finally, we use several tricks to get the geodesics and explore the divergence performance of them by investigating the Jacobi vector field.
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