Estimation in a fluctuating medium and power-law distributions

TL;DR

This paper links recent estimation results and classical distribution theory to explain the widespread occurrence of power law distributions, introducing a multivariate central limit theorem as a novel contribution.

Contribution

It combines recent estimation insights with classical Fisher results to explain power law ubiquity and proposes a new multivariate central limit theorem as an alternative.

Findings

Provides a theoretical explanation for power law distributions in fluctuating media.

Introduces a multivariate version of the central limit theorem.

Offers an alternative to existing multivariate CLT results.

Abstract

We show how recent results by Bening and Korolev in the context of estimation, when linked with a classical result of Fisher concerning the negative binomial distribution, can be used to explain the ubiquity of power law probability distributions. Beck, Cohen and others have provided plausible mechanisms explaining how power law probability distributions naturally emerge in scenarios characterized by either finite dimension or fluctuation effects. This paper tries to further contribute to such an idea. As an application, a new and multivariate version of the central limit theorem is obtained that provides a convenient alternative to the one recently presented in [S. Umarov, C. Tsallis, S. Steinberg, cond-mat/0603593].