The Distributions in Nature and Entropy Principle
Abstract
The derivation of the maximum entropy distribution of particles in boxes yields two kinds of distributions: a "belllike" distribution and a longtail distribution. The first one is obtained when the ratio between particles and boxes is low, and the second one  when the ratio is high. The obtained long tail distribution yields correctly the empirical Zipf law, Pareto's 20:80 rule and Benford's law. Therefore, it is concluded that the long tail and the "belllike" distributions are outcomes of the tendency of statistical systems to maximize entropy.
 Publication:

arXiv eprints
 Pub Date:
 July 2009
 arXiv:
 arXiv:0907.4852
 Bibcode:
 2009arXiv0907.4852K
 Keywords:

 Computer Science  Discrete Mathematics;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 19 pages 5 figures