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Ciofalo, M (2009)

Entropy, Benford’s first digit law, and the distribution of everything

Dipartimento di Ingegneria Nucleare, Università degli Studi di Palermo, Italy.

ISSN/ISBN: Not available at this time. DOI: Not available at this time.

Abstract: ABSTRACT: The history of the so called “Benford’s Law”, which concerns the distribution of the first significant digits in “natural” sets of measurements, is summarized, and its relation with exponential rank-size distributions (associated with geometric progressions of naturally-occurring quantities) is outlined. The physical significance of alternative distributions is then discussed by considering also the associated probability density functions, and it is shown that – under appropriate assumptions – exponential rank-size distributions can be derived from a maximum-entropy principle (in the information-theory sense as introduced by Shannon). Finally, naturally-occurring samples (e.g., surface areas of islands) are considered in detail and it is shown that they closely follow exponential rank-size distributions and satisfy both Benford’s law and appropriately formulated principles of uniform probability density and maximum information entropy.

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Reference Type: E-Print

Subject Area(s): Applied Mathematics, Statistics