### Burgos, A and Santos, A (2021)

#### The Newcomb–Benford law: Do physicists use more frequently the key 1 than the key 9?

Preprint arXiv:2101.12068 [physics.pop-ph]; last accessed February 15, 2021.

**ISSN/ISBN:** Not available at this time.
**DOI:** Not available at this time.

**Abstract:** The Newcomb--Benford law, also known as the first-digit law, gives the probability distribution associated with the first digit of a dataset, so that the first significant digit has a probability of 30.1 % of being 1 and 4.58 % of being 9. This law can be extended to the second and next significant digits. In this article, an introduction to the discovery of the law, its derivation from the scale invariance property, as well as some applications and examples, are presented. Additionally, a simple dynamic model simulating how an initial dataset changes if sequentially multiplied by a factor 2 is proposed. Within this model, it is proved that the first-digit distribution of the generated datasets irreversibly converges to the Newcomb--Benford law.

**Bibtex:**

```
@misc{,
title={The Newcomb--Benford law: Do physicists use more frequently the key 1 than the key 9?},
author={Andrea Burgos and Andrés Santos},
year={2021},
eprint={2101.12068},
archivePrefix={arXiv},
primaryClass={physics.pop-ph},
url = {https://arxiv.org/abs/2101.12068},
}
```

**Reference Type:** Preprint

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