2003/05/11 by Sumiyoshi Abe · 85 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Distribution (mathematics) #Divergence (linguistics) #Fractal #Fractional Differential Equations Solutions #Geometry #Information geometry #Limit (mathematics) #Mathematical analysis #Mathematics #Metric (unit) #Multifractal system #Physics #Probabilistic logic #Probability distribution #Statistical Mechanics and Entropy #Statistical manifold #Statistical mechanics #Statistical model #Statistical parameter #Statistical physics #Statistics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.68.031101
published in Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 68(3), 031101 (American Physical Society) · 12 pages, no figures
arxiv created 2003/05/11 · openalex publication_date 2003/09/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Given an original distribution, its statistical and probabilistic attributes may be scanned using the associated escort distribution introduced by Beck and Schlögl 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 Cramér-Rao inequality leads to a fundamental limit for the precision of the statistical estimate of the order of the escort distribution. We also show quantitatively that it is inappropriate to use the original distribution instead of the escort distribution for calculating the expectation values of physical quantities in nonextensive statistical mechanics.