Information theory and generalized statistics

TL;DR

This paper explores generalized statistical measures derived from information theory, such as Renyi's, Fisher's, and Tsallis's, and discusses their applications to complex systems with fractal structures.

Contribution

It provides a unifying framework connecting various generalized statistics through information theory and examines their relevance to fractal systems.

Findings

Generalized statistics can describe systems with fractal structures.

Information theory offers a unifying approach to different statistical measures.

Applications include analyzing complex, multi-fractal systems.

Abstract

We present a discussion of generalized statistics based on Renyi's, Fisher's and Tsallis's measures of information. The unifying conceptual framework which we employ here is provided by information theory. Important applications of generalized statistics to systems with (multi-)fractal structure are examined.