Estimation in a fluctuating medium and power-law distributions

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].