%0 Journal Article
%T Heavy-Tailed Distributions Generated by Randomly Sampled Gaussian, Exponential and Power-Law Functions
%A Frederic von Wegner
%J Applied Mathematics
%P 2050-2056
%@ 2152-7393
%D 2014
%I Scientific Research Publishing
%R 10.4236/am.2014.513198
%X A simple stochastic mechanism that produces exact and approximate
power-law distributions is presented. The model considers radially symmetric
Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Randomly sampling these functions with a
radially uniform sampling scheme produces heavy-tailed distributions. For
two-dimensional Gaussians and one-dimensional exponential functions, exact
power-laws with exponent ¨C1 are obtained. In other cases, densities with an
approximate power-law behaviour close to the origin arise. These densities are
analyzed using Pad¨¦ approximants in order to show the approximate power-law behaviour.
If the sampled function itself follows a power-law with exponent ¨C¦Á, random sampling leads to densities
that also follow an exact power-law, with exponent -n/a ¨C 1. The presented mechanism shows that power-laws can arise in generic
situations different from previously considered specialized systems such as
multi-particle systems close to phase transitions, dynamical systems at
bifurcation points or systems displaying self-organized criticality. Thus, the
presented mechanism may serve as an alternative hypothesis in system
identification problems.
%K Heavy-Tailed Distributions
%K Random Sampling
%K Gaussian
%K Exponential
%K Power-Law
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=47930