Fractal probability laws

  • Eliazar I
  • Klafter J
  • 12


    Mendeley users who have this article in their library.
  • 17


    Citations of this article.


We explore six classes of fractal probability laws defined on the positive half-line: Weibull, Frechét, Lévy, hyper Pareto, hyper beta, and hyper shot noise. Each of these classes admits a unique statistical power-law structure, and is uniquely associated with a certain operation of renormalization. All six classes turn out to be one-dimensional projections of underlying Poisson processes which, in turn, are the unique fixed points of Poissonian renormalizations. The first three classes correspond to linear Poissonian renormalizations and are intimately related to extreme value theory (Weibull, Frechét) and to the central limit theorem (Lévy). The other three classes correspond to nonlinear Poissonian renormalizations. Pareto's law--commonly perceived as the "universal fractal probability distribution"--is merely a special case of the hyper Pareto class.

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document


  • Iddo Eliazar

  • Joseph Klafter

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free