Geometry of escort distributions

Details Geometry of escort distributions Geometry of escort distributions

2003-05-11

arxiv.org/abs/cond-mat/0305231v1

Physics

Condensed Matter

Statistical Mechanics

12 pages, no figures

Scientific paper

10.1103/PhysRevE.68.031101

Given an original distribution, its statistical and probabilistic attributs may be scanned by the associated escort distribution introduced by Beck and Schlogl and employed in the formulation of nonextensive statistical mechanics. Here, the geometric structure of the one-parameter family of the escort distributions is studied based on the Kullback-Leibler divergence and the relevant Fisher metric. It is shown that the Fisher metric is given in terms of the generalized bit-variance, which measures fluctuations of the crowding index of a multifractal. The Cramer-Rao inequality leads to the fundamental limit for precision of statistical estimate of the order of the escort distribution. It is also quantitatively discussed how inappropriate it is to use the original distribution instead of the escort distribution for calculating the expectation values of physical quantities in nonextensive statistical mechanics.

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