### Kossovsky, AE (2006)

#### Towards a Better Understanding of the Leading Digits Phenomena

posted December 21, 2006 on arXiv:math/0612627.

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

**Abstract:** This article on leading digits (Benford's Law) contains the following: (I) An attempt at a comprehensive account on the leading digits phenomena, incorporating many of its existing explanations, proofs, and differing points of view. (II) The finding that leading digits of random numbers derived from a chain of distributions that are linked via parameter selection are logarithmic in the limit as the number of sequences approaches infinity, and that empirically only around 5 or 6 sequences of such a distribution chain are needed to obtain results that are close enough to the logarithmic (i.e. rapid convergence). (III) An outright exact logarithmic behavior for a 2-sequence chain whenever parametrical density is exactly logarithmic. (IV) An account on the existence of singularities in exponential growth rates with regards to the leading digits distributions of their series. (V) An account on several distributions that are intrinsically logarithmic or approximately so. (VI) A conceptual justification of Flehinger's iterated averaging scheme - an algorithm that was presented without any clear motivation. (VII) A note on the close relationship of Flehinger's scheme and the chain of distribution to Hill's super distribution. (VIII) A conceptual argument justifying the scale invariance principle - a principle invoked in derivations of Benford's law. (IX) A note on the intimate connection between one-sided tail to the right in density distributions and logarithmic leading digit behavior.

**Bibtex:**

```
@misc{,
AUTHOR = {Kossovsky, Alex Ely},
TITLE = {Towards a better understanding of the leading digits phenomena},
HOWPUBLISHED = {\url{http://arxiv.org/abs/math/0612627}},
YEAR = {2006},
NOTE = {last accessed Mar 28, 2016},
}
```

**Reference Type:** Preprint

**Subject Area(s):** Statistics