Preprint.
ISSN/ISBN: Not available at this time. DOI: Not available at this time.
Abstract: Benford’s law is a statement about the frequency that each digit arises as the leading digit of numbers in a dataset. It is satisfied by various common integer sequences, such as the Fibonacci numbers, the factorials, and the powers of most integers. In this paper, we prove that integer sequences resulting from a random integral decomposition process (which we model as discrete “stick breaking”) subject to a certain congruence stopping condition approaches Benford distribution asymptotically. We also observe that the congruence stopping condition imposed is sharp; namely, once we let the stopping condition deviate above or below the given threshold, the resulting sequence fails to obey Benford’s law.
Bibtex:
@misc{,
author = {Xinyu Fang and Steven J. Miller and Maxwell Sun and Amanda Verga},
title = {Benford’s Law and Random Integer Decomposition with Congruence Stopping Condition},
year = {2024},
url = {https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/Benford_SMALL23_Fragmentation_ContDisc_V22.pdf},
}
Reference Type: Preprint
Subject Area(s): Number Theory