TY - JOUR
T1 - Explaining the uneven distribution of numbers in nature
T2 - The laws of Benford and Zipf
AU - Pietronero, L.
AU - Tosatti, E.
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.
PY - 2001/4/1
Y1 - 2001/4/1
N2 - 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.
AB - 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.
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U2 - 10.1016/S0378-4371(00)00633-6
DO - 10.1016/S0378-4371(00)00633-6
M3 - Article
AN - SCOPUS:0034825396
SN - 0378-4371
VL - 293
SP - 297
EP - 304
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 1-2
ER -