Maximum Entropy Formalism, Fractals, Scaling Phenomena, and 1/f
Noise: A Tale of Tails
Elliott W. Montroll and Michael F. Shlesinger
Journal of Statistical Physics , vol. 32, no.2, 209-230(1983)
Abstract
In this report on examples of distribution functions with long tails we
(a) show that the derivation of distribution with inverse power tails
from a maximum entropy formalism would be a consequence only of an
unconventional auxiliary condition that involves the specification of
the average value of a complicated logarithmic functions, (b) review several
models that yield log-normal distributions, (c) show that log normal
distributions may mimic 1/f noise over a certain range, and (d) present
an amplification model to show how log-normal personal income distributions
are transformed into inverse power (Pareto) distributions in the high income
range.
math model of 1/f section