### Jasak, Z (2017)

#### Sum invariance testing and some new properties of Benford's law

Doctorial Dissertation, University of Tuzla, Bosnia and Herzegovina.

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

**Abstract:** Benford's law is logarithmic law which describes probabilities of leading digits or group of digits in numbers, named after Frank Albert Benford (1938) who formulated mathematical model of this probability. Before him, the same observation was made by Simon Newcomb (1881). This law has changed usual preasumption of equal probability of each digit on each position in number. Main goals of this text are to present some new properties of Benford's law, to extend sum invariance property on second position and other groups of digitis and to propose tests for sum invariance property. New properties of Benford's law are close connection with arithmetic sequencies and harmonic property of Benford-like probabilities. Some additional standard nonparametric tests for sum invariance property and frequencies of digits are presented.

**Bibtex:**

```
@phdthesis{,
author = {Jasak, Zoran},
year = {2017},
month = {10},
pages = {},
title = {Sum invariance testing and some new properties of Benford's law}
institution = {University of Tuzla, Bosnia and Herzegovina},
}
```

**Reference Type:** Thesis

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