View Complete Reference

Wojcik, MR (2014)

A characterization of Benfordís law through generalized scale-invariance

Mathematical Social Sciences, Volume 71, September 2014, pp. 1Ė5.

ISSN/ISBN: Not available at this time. DOI: 10.1016/j.mathsocsci.2014.03.006



Abstract: If X is uniformly distributed modulo 1 and Y is independent of X then Y+X is also uniformly distributed modulo 1. We prove a converse for any continuous random variable Y (or a reasonable approximation to a continuous random variable) so that if X and Y+X are equally distributed modulo 1 and Y is independent of X then X is uniformly distributed modulo 1 (or approximates the uniform distribution equally reasonably). This translates into a characterization of Benfordís law through a generalization of scale-invariance: from multiplication by a constant to multiplication by an independent random variable.


Bibtex:
@article {, AUTHOR = {Wojcik, MMichal Ryszard}, TITLE = {A characterization of Benfordís law through generalized scale-invariance}, JOURNAL = {Mathematical Social Sciences}, YEAR = {2014}, VOLUME = {71}, PAGES = {1--5}, MONTH = {September}, DOI = {10.1016/j.mathsocsci.2014.03.006}, }


Reference Type: Journal Article

Subject Area(s): Probability Theory, Social Sciences, Statistics