## View Complete Reference

### Ozawa, K (2019)

#### Continuous Distributions on (0, ∞) Giving Benford’s Law Exactly

Preprint arXiv:1905.02031 [math.PR]; last accessed June 6, 2019.

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

Abstract: Benford's law is a famous law in statistics which states that the leading digits of random variables in diverse data sets appear not uniformly from 1 to 9; the probability that d (d=1,...,9) appears as a leading digit is given by \log_{10}(1+1/d). This paper shows the existence of a random variable with a smooth probability density on (0,\infty) whose leading digit distribution follows Benford's law exactly. To construct such a distribution the error theory of the trapezoidal rule is used.

Bibtex:
@ARTICLE{, author = {{Ozawa}, Kazufumi}, title = "{Continuous Distributions on $(0,\,\infty)$ Giving Benford's Law Exactly}", journal = {arXiv e-prints}, year = "2019", month = "May", eid = {arXiv:1905.02031}, pages = {arXiv:1905.02031}, }

Reference Type: Preprint

Subject Area(s): Probability Theory, Statistics