Indexing metadata

Random number sequences and the first digit phenomenon


 
Dublin Core PKP Metadata Items Metadata for this Document
 
1. Title Title of document Random number sequences and the first digit phenomenon
 
2. Creator Author's name, affiliation, country Bruno Massé; Université du Littoral Côte d'Opale; France
 
2. Creator Author's name, affiliation, country Dominique Schneider; Université du Littoral Côte d'Opale; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Benford's law; weak convergence; mantissa; density
 
3. Subject Subject classification 60B10; 11B05; 11K99
 
4. Description Abstract The sequences of mantissa of positive integers and of prime numbers are known not to be distributed as Benford's law in the sense of the natural density. We show that we can correct this defect by selecting the integers or the primes by means of an adequate random process and we investigate the rate of convergence. Our main tools are uniform bounds for deterministic and random trigonometric polynomials. We then adapt the random process to prove the same result for logarithms and iterated logarithms of integers. Finally we show that, in many cases, the mantissa law of the $n$th randomly selected term converges weakly to the Benford's law.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2012-10-04
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/1900
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-1900
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
15. Rights Copyright and permissions The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.

Summary of the Creative Commons Attribution License

You are free
  • to copy, distribute, display, and perform the work
  • to make derivative works
  • to make commercial use of the work
under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.