Maximum Likelihood Estimation for q-Exponential (Tsallis) Distributions

TL;DR

This paper explains how to use maximum likelihood estimation to determine parameters of q-exponential distributions and explores their connection to Pareto distributions.

Contribution

It provides a clear methodology for applying maximum likelihood to q-exponential distributions and clarifies their relationship with classical Pareto distributions.

Findings

Maximum likelihood estimation can be effectively applied to q-exponential distributions.

The relationship between q-exponential and Pareto distributions is elucidated.

The note offers practical guidance for parameter estimation in non-extensive statistical mechanics.

Abstract

This expository note describes how to apply the method of maximum likelihood to estimate the parameters of the ``$q$-exponential'' distributions introduced by Tsallis and collaborators. It also describes the relationship of these distributions to the classical Pareto distributions.