### Eliazar, II (2013)

#### Benford's Law: A Poisson Perspective

Physica A 392(16) pp. 3360–3373.

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

**Abstract:** Benford’s 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 Benford’s law from a Poisson perspective, considering ensembles of positive numerical values governed by Poisson-process statistics. We show that this Poisson setting naturally accommodates Benford’s law and: (i) establish a Poisson characterization and a Poisson multidigit-extension of Benford’s law; (ii) study a system-invariant leading-digit distribution which generalizes Benford’s 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 Fréchet extreme-value distributions, and distinguish the special role of Benford’s 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 Benford’s 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