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Generalizing Benford's Law Using Power Laws : Application to Integer Sequences
Author
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-08-10
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
Many distributions for first digits of integer sequences are not Benford.
A simple method to derive parametric analytical extensions of Benford's law for first digits of numerical data is proposed.
Two generalized Benford distributions are considered, namely, the two-sided power Benford (TSPB) distribution, which has been introduced in Hürlimann (2003), and the new Pareto Benford (PB) distribution.
Based on the minimum chi-square estimators, the fitting capabilities of these generalized Benford distributions are illustrated and compared at some interesting and important integer sequences.
In particular, it is significant that much of the analyzed integer sequences follow with a high P-value the generalized Benford distributions.
While the sequences of prime numbers less than 1000, respectively, 10 000 are not at all Benford or TSPB distributed, they are approximately PB distributed with high P-values of 93.3% and 99.9% and reveal after a further deeper analysis of longer sequences a new interesting property.
On the other side, Benford's law of a mixing of data sets is rejected at the 5% significance level while the PB law is accepted with a 93.6% P-value, which improves the P-value of 25.2%, which has been obtained previously for the TSPB law.
American Psychological Association (APA)
Hürlimann, Werner. 2009. Generalizing Benford's Law Using Power Laws : Application to Integer Sequences. International Journal of Mathematics and Mathematical Sciences،Vol. 2009, no. 2009, pp.1-10.
https://search.emarefa.net/detail/BIM-512334
Modern Language Association (MLA)
Hürlimann, Werner. Generalizing Benford's Law Using Power Laws : Application to Integer Sequences. International Journal of Mathematics and Mathematical Sciences No. 2009 (2009), pp.1-10.
https://search.emarefa.net/detail/BIM-512334
American Medical Association (AMA)
Hürlimann, Werner. Generalizing Benford's Law Using Power Laws : Application to Integer Sequences. International Journal of Mathematics and Mathematical Sciences. 2009. Vol. 2009, no. 2009, pp.1-10.
https://search.emarefa.net/detail/BIM-512334
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-512334