Benford’s law and distribution functions of sequences in (0, 1)

Applying the theory of distribution functions of sequences x n ∈ [0, 1], n = 1, 2, ..., we find a functional equation for distribution functions of a sequence x n and show that the satisfaction of this functional equation for a sequence x n is equivalent to the fact that the sequence x n to satisfie...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical Notes 2010-10, Vol.88 (3-4), p.449-463
Main Authors: Baláž, V., Nagasaka, K., Strauch, O.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Applying the theory of distribution functions of sequences x n ∈ [0, 1], n = 1, 2, ..., we find a functional equation for distribution functions of a sequence x n and show that the satisfaction of this functional equation for a sequence x n is equivalent to the fact that the sequence x n to satisfies the strong Benford law. Examples of distribution functions of sequences satisfying the functional equation are given with an application to the strong Benford law in different bases. Several direct consequences from uniform distribution theory are shown for the strong Benford law.
ISSN:0001-4346
1573-8876
DOI:10.1134/S0001434610090178