### Khosravani, A and Rasinariu, C (2012)

#### Transformation invariance of Benford variables and their numerical modeling

Recent Researches in Automatic Control and Electronics - Proceedings of the 14th International Conference on Automatic Control, Modelling & Simulation (ACMOS '12) and
Proceedings of the 11th International Conference on Microelectronics, Nanoelectronics.

**ISSN/ISBN:** 978-1-61804-080-0
**DOI:** Not available at this time.

**Abstract:** A random variable is Benford distributed if the occurrence frequency of its most significant digit is P(d) = log10(1 + 1/d).
Many empirical data sets obey this law with various degrees of accuracy .In this paper we analyze random variables X such that Y = 10X satisfies Benford's law exactly. We introduce a family of transformations on X that leave the digit distribution of Y invariant. Thus we identify new conditions for exact Benford conformance,and construct novel examples of such random variables. The Mathematica simulations strongly support our theoretical results.

**Bibtex:**

```
@InProceedings {,
AUTHOR = {Khosravani, A. and Rasinariu, C.},
TITLE = {Transformation invariance of Benford variables and their numerical modeling},
BOOKTITLE = {Recent Researches in Automatic Control and Electronics - Proceedings of the 14th International Conference on Automatic Control, Modelling & Simulation (ACMOS '12) and Proceedings of the 11th International Conference on Microelectronics, Nanoelectronics},
YEAR = {2012},
ISBN = {978-1-61804-080-0},
PAGES = {57--61},
}
```

**Reference Type:** Conference Paper

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