Explaining the uneven distribution of numbers in nature: the laws of Benford and Zipf
Explaining the uneven distribution of numbers in nature: the laws of Benford and Zipf
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DOI：
10.1016/s0378-4371(00)00633-6
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发表时间：
2001-04-01
期刊：
影响因子：
3.3
通讯作者：
Vespignani, A
中科院分区：
文献类型：
--
作者：
Pietronero, L;Tosatti, E;Vespignani, A
从非常不同的来源获得的数字序列中的第一位数的分布显示出明显的不对称性，有利于小数字，这就是本福德定律的名称。我们详细分析了这一属性的不同数据集，并给出了一般的解释的起源本福德定律的乘法过程。我们表明，这一法律也可以推广到一系列的数字产生的更复杂的系统，如目录的地震活动。最后，我们推导出广义Benford定律和流行的Zipf定律之间的关系，它们表征了秩序统计量，并已广泛应用于从城市人口到语言学的许多问题。(C)出版社：Elsevier Science B.V.
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. (C) 2001 Published by Elsevier Science B.V.