  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].
