Explaining the uneven distribution of numbers in nature: The laws of Benford and Zipf

L. Pietronero; E. Tosatti; V. Tosatti; A. Vespignani

doi:10.1016/S0378-4371(00)00633-6

Explaining the uneven distribution of numbers in nature: The laws of Benford and Zipf

L. Pietronero, E. Tosatti, V. Tosatti, A. Vespignani

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The distribution of first digits in numbers series obtained from very different origins shows a marked asymmetry in favor of small digits that goes under the name of Benford's law. We analyze in detail this property for different data sets and give a general explanation for the origin of the Benford's law in terms of multiplicative processes. We show that this law can be also generalized to series of numbers generated from more complex systems like the catalogs of seismic activity. Finally, we derive a relation between the generalized Benford's law and the popular Zipf's law which characterize the rank order statistics and has been extensively applied to many problems ranging from city population to linguistics.

Original language	English (US)
Pages (from-to)	297-304
Number of pages	8
Journal	Physica A: Statistical Mechanics and its Applications
Volume	293
Issue number	1-2
DOIs	https://doi.org/10.1016/S0378-4371(00)00633-6
State	Published - Apr 1 2001

ASJC Scopus subject areas

Statistics and Probability
Condensed Matter Physics

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10.1016/S0378-4371(00)00633-6

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title = "Explaining the uneven distribution of numbers in nature: The laws of Benford and Zipf",

abstract = "The distribution of first digits in numbers series obtained from very different origins shows a marked asymmetry in favor of small digits that goes under the name of Benford's law. We analyze in detail this property for different data sets and give a general explanation for the origin of the Benford's law in terms of multiplicative processes. We show that this law can be also generalized to series of numbers generated from more complex systems like the catalogs of seismic activity. Finally, we derive a relation between the generalized Benford's law and the popular Zipf's law which characterize the rank order statistics and has been extensively applied to many problems ranging from city population to linguistics.",

author = "L. Pietronero and E. Tosatti and V. Tosatti and A. Vespignani",

note = "Funding Information: We thank G. Mussardo for useful discussions and comments. We are grateful to P. Shebalin for pointing out to us the earthquakes catalog. L.P. thanks the hospitality of ICTP where part of this work has been completed. L.P and A.V. acknowledge partial support from the TMR European Program ERBFMRXCT980183. ",

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AU - Tosatti, V.

AU - Vespignani, A.

N1 - Funding Information: We thank G. Mussardo for useful discussions and comments. We are grateful to P. Shebalin for pointing out to us the earthquakes catalog. L.P. thanks the hospitality of ICTP where part of this work has been completed. L.P and A.V. acknowledge partial support from the TMR European Program ERBFMRXCT980183.

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Explaining the uneven distribution of numbers in nature: The laws of Benford and Zipf

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