Related papers: Does human speech follow Benford's Law?
Prime numbers seem to distribute among the natural numbers with no other law than that of chance, however its global distribution presents a quite remarkable smoothness. Such interplay between randomness and regularity has motivated sci-…
We show how Benford's Law (BL) for first, second, ..., digits, emerges from the distribution of digits of numbers of the type $a^{R}$, with $a$ any real positive number and $R$ a set of real numbers uniformly distributed in an interval $[…
Benford's law is a statistical inference to predict the frequency of significant digits in naturally occurring numerical databases. In such databases this law predicts a higher occurrence of the digit 1 in the most significant place and…
We show that the frequency distribution of the first significant digits of the numbers in the data sets generated from a large class of measures of quantum correlations, which are either entanglement measures, or belong to the…
Large Language Models (LLMs) exhibit impressive performance on complex reasoning tasks, yet they frequently fail on basic numerical problems, producing incorrect outputs. Inspired by Benford's Law, a statistical pattern in which lower…
Suppose you look at today's stock prices and bet on the value of the first digit. One could guess that a fair bet should correspond to the frequency of $1/9 = 11.11%$ for each digit from 1 to 9. This is by no means the case, and one can…
Exponential growth occurs when the growth rate of a given quantity is proportional to the quantity's current value. Surprisingly, when exponential growth data is plotted as a simple histogram disregarding the time dimension, a remarkable…
Fix a base B and let zeta have the standard exponential distribution; the distribution of digits of zeta base B is known to be very close to Benford's Law. If there exists a C such that the distribution of digits of C times the elements of…
It has long been known that sequences such as the powers of $2$ and the factorials satisfy Benford's Law; that is, leading digits in these sequences occur with frequencies given by $P(d)=\log_{10}(1+1/d)$, $d=1,2,\dots,9$. In this paper, we…
Benford's Law describes the prevalence of small numbers as the leading digits of numbers in many sets of integers. We prove a variant of Benford's law for many positive-density subsets of the primes. This follows from a more general result…
Benford's law describes a common phenomenon among many naturally occurring data sets and distributions in which the leading digits of the data are distributed with the probability of a first digit of $d$ base $B$ being…
We found that in transition arrays of complex atomic spectra, the strengths of electric-dipolar lines obey Benford's law, which means that their significant digits follow a logarithmic distribution favoring the smallest values. This…
The first digit law, also known as Benford's law or the significant digit law, is an empirical phenomenon that the leading digit of numbers from real world sources favors small ones in a form $\log(1+{1}/{d})$, where $d=1, 2, ..., 9$. Such…
The occurrence of digits one through nine as the leftmost nonzero digit of numbers from real world sources is often not uniformly distributed, but instead, is distributed according to a logarithmic law, known as Benford's law. Here, we…
The intriguing law of anomalous numbers, also named Benford's law, states that the significant digits of data follow a logarithmic distribution favoring the smallest values. In this work, we test the compliance with this law of the atomic…
The importance of statistical patterns of language has been debated over decades. Although Zipf's law is perhaps the most popular case, recently, Menzerath's law has begun to be involved. Menzerath's law manifests in language, music and…
That the logarithmic distribution manifests itself in the random as well as in the deterministic (multiplication processes) has long intrigued researchers in Benford's Law. In this article it is argued that it springs from one common…
Benford's Law predicts that the first significant digit on the leftmost side of numbers in real-life data is proportioned between all possible 1 to 9 digits approximately as in LOG(1 + 1/digit), so that low digits occur much more frequently…
We explain Kossovsky's generalization of Benford's law which is a formula that approximates the distribution of leftmost digits in finite sequences of natural data and apply it to six sequences of data including populations of US cities and…
The occurrence of the nonzero leftmost digit, i.e., 1, 2, ..., 9, of numbers from many real world sources is not uniformly distributed as one might naively expect, but instead, the nature favors smaller ones according to a logarithmic…