Abstract
In this report on examples of distribution functions with long tails we (a) show that the derivation of distributions with inverse power tails from a maximum entropy formalism would be a consequence only of an unconventional auxilliary condition that involves the specification of the average value of a complicated logarithmic function, (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.
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Montroll, E.W., Shlesinger, M.F. Maximum entropy formalism, fractals, scaling phenomena, and 1/f noise: A tale of tails. J Stat Phys 32, 209–230 (1983). https://doi.org/10.1007/BF01012708
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DOI: https://doi.org/10.1007/BF01012708