Estimation in a fluctuating medium and power-law distributions

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 Letter 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].