Math arXiv:1203.2518; posted 19 Apr 2012.

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

- For online information, click here.
- For additional online information, click here.

**Abstract:** This is a detailed survey which mainly presents the Pinkham-Feller way. I added some new points to the first version [V2] and I suppressed "Examples" devoted to Gamma, FrÃ©chet and Weibull laws. Theorem 2 is a bit more general (no assumption of density: this answers a question of T. Hill). Section 10 is new and devoted to an argument (PoincarÃ©, Fewster) about the effect of high frequencies oscillations. Maybe many works, many efforts, have been devoted to the study of a sufficient condition of poor value: see Sections 7 and 11. The final Section gives some suggestions.

**Bibtex:**

```
@unpublished{,
AUTHOR = {Valadier, Michel},
TITLE = {The Benford phenomenon for random variables. Discussion of Feller's way},
YEAR = {2012},
DATE = {19 Apr 2012},
EPRINT = {http://arxiv.org/abs/1203.2518},
}
```

**Reference Type:** Preprint

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