### The Distributions in Nature and Entropy Principle

#### Abstract

**Abstract. **The derivation of the maximum entropy distribution of particles in boxes yields two kinds of distributions: a "bell-like" distribution and a long-tail 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 "bell-like" distributions are outcomes of the tendency of statistical systems to maximize entropy.

**Keywords.** Maximum Entropy, Long tail distribution, 20:80 Pareto's rule, Zipf Law, Benford's law, Bell-like distribution.

**JEL. **C62**.**

#### Keywords

#### References

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DOI: http://dx.doi.org/10.1453/ter.v3i4.1122

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