### Cerqueti, R and Maggi, M (2021)

#### Data validity and statistical conformity with Benford’s Law

Chaos, Solitons & Fractals 144, p. 110740
.

**ISSN/ISBN:** Not available at this time.
**DOI:** 10.1016/j.chaos.2021.110740

**Abstract:** Benford’s Law is a statistical regularity of a large number of datasets; assessing the compliance of a large dataset with the Benford’s Law is a theme of remarkable relevance, mainly for its practical consequences. Such a task can be faced by introducing a statistical distance concept between the empirical distribution of the data and the random variable associated with Benford’s Law. This paper deals with the problem of measuring the compliance of a random variable – which can be seen as describing the empirical distribution of a collection of data – with the Benford’s Law. It proposes a statistical methodology for detecting the critical values related to conformity/nonconformity with Benford’s Law in some well-established cases of statistical distance. The followed approach is grounded on the proper selection of a family of parametric random variables – the lognormal distribution, in our case – and of a reference statistical distance concept – mean absolute deviation. A discussion of the obtained results is carried out on the ground of the existing literature. Moreover, some open problems are also presented.

**Bibtex:**

```
@article{,
title = {Data validity and statistical conformity with Benford’s Law},
journal = {Chaos, Solitons \& Fractals},
volume = {144},
pages = {110740},
year = {2021},
issn = {0960-0779},
doi = {10.1016/j.chaos.2021.110740},
url = {https://www.sciencedirect.com/science/article/pii/S096007792100093X},
author = {Roy Cerqueti and Mario Maggi},
}
```

**Reference Type:** Journal Article

**Subject Area(s):** Probability Theory, Statistics