Law of Error in Tsallis Statistics
Hiroki Suyari, Makoto Tsukada
TL;DR
This paper generalizes Gauss' law of error within Tsallis statistics, deriving a Tsallis distribution as a nonextensive extension of the Gaussian distribution using q-logarithm and q-exponential functions.
Contribution
It introduces a novel approach to error law generalization by applying q-deformed operations, connecting Tsallis entropy with error distribution modeling.
Findings
Derives Tsallis distribution as a nonextensive error law
Utilizes q-logarithm and q-exponential functions in likelihood formulation
Extends classical error law to multifractal systems
Abstract
Gauss' law of error is generalized in Tsallis statistics such as multifractal systems, in which Tsallis entropy plays an essential role instead of Shannon entropy. For the generalization, we apply the new multiplication operation determined by the q-logarithm and the q-exponential functions to the definition of the likelihood function in Gauss' law of error. The maximum likelihood principle leads us to finding Tsallis distribution as nonextensively generalization of Gaussian distribution.
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Taxonomy
TopicsStatistical Mechanics and Entropy · Advanced Statistical Methods and Models · Complex Systems and Time Series Analysis