Generalized Non-extensive Statistical Distributions

TL;DR

This paper derives generalized statistical distributions using Tsallis' and Renyi's entropy measures, extending classical distributions with a parameter q, and finds they are nearly indistinguishable except for a constant.

Contribution

It introduces a unified approach to derive generalized distributions based on non-extensive entropy measures, expanding the classical framework.

Findings

Generalized distributions depend on a parameter q.

In the limit q=1, distributions revert to classical forms.

Generalized Tsallis' and Renyi distributions are nearly indistinguishable.

Abstract

We find the value of constants related to constraints in characterization of some known statistical distributions and then we proceed to use the idea behind maximum entropy principle to derive generalized version of this distributions using the Tsallis' and Renyi information measures instead of the well-known Bolztmann-Gibbs-Shannon. These generalized distributions will depend on q (real number) and in the limit (q=1) we obtain the "classical" ones. We found that apart from a constant, generalized versions of statistical distributions following Tsallis' or Renyi are undistinguishable.