Sulei I. R. Costa, Sandra A. Santos, João E. Strapasson
This paper is a strongly geometrical approach to the Fisher distance, which is a measure of dissimilarity between two probability distribution functions. This, as well as other divergence measures, are also used in many applications to establish a proper data average. It focuses on statistical models of the normal probability distribution functions and takes advantage of the connection with the classical hyperbolic geometry to derive closed forms for the Fisher distance in several cases. Connections with the well-known Kullback-Leibler divergence measure are also devised. The main purpose is to widen the range of possible interpretations and relations of the Fisher distance and its associated geometry for the prospective applications, in particular to information theory.
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http://arxiv.org/abs/1210.2354
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