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Eliazar, II (2013)

Benford's Law: A Poisson Perspective

Physica A 392(16) pp. 3360Ė3373.

ISSN/ISBN: Not available at this time. DOI: 10.1016/j.physa.2013.03.057



Abstract: Benfordís law is a counterintuitive statistical law asserting that the distribution of leading digits, taken from a large ensemble of positive numerical values that range over many orders of scale, is logarithmic rather than uniform (as intuition suggests). In this paper we explore Benfordís law from a Poisson perspective, considering ensembles of positive numerical values governed by Poisson-process statistics. We show that this Poisson setting naturally accommodates Benfordís law and: (i) establish a Poisson characterization and a Poisson multidigit-extension of Benfordís law; (ii) study a system-invariant leading-digit distribution which generalizes Benfordís law, and establish a Poisson characterization and a Poisson multidigit-extension of this distribution; (iii) explore the universal emergence of the system-invariant leading-digit distribution, couple this universal emergence to the universal emergence of the Weibull and Frťchet extreme-value distributions, and distinguish the special role of Benfordís law in this universal emergence; (iv) study the continued-fractions counterpart of the system-invariant leading-digit distribution, and establish a Poisson characterization of this distribution; and (v) unveil the elemental connection between the system-invariant leading-digit distribution and its continued- fractions counterpart. This paper presents a panoramic Poisson approach to Benfordís law, to its system-invariant generalization, and to its continued-fractions counterpart.


Bibtex:
@article{, title = "Benford's law: A Poisson perspective", journal = "Physica A: Statistical Mechanics and its Applications ", volume = "392", number = "16", pages = "3360 - 3373", year = "2013", note = "", issn = "0378-4371", doi = "http://dx.doi.org/10.1016/j.physa.2013.03.057", url = "http://www.sciencedirect.com/science/article/pii/S0378437113002902", author = "Iddo I. Eliazar", }


Reference Type: Journal Article

Subject Area(s): Statistics