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Explaining the uneven distribution of numbers in nature: the laws of Benford and Zipf. (English) Zbl 0978.60032
Summary: 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 have been extensively applied to many problems ranging from city population to linguistics.

60G07 General theory of stochastic processes
Full Text: DOI
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