Related papers: Benford's law in atomic spectra and opacity databa…
We determine the leading digit laws for the matrix components of a linear Lie group $G$. These laws generalize the observations that the normalized Haar measure of the Lie group $\mathbb{R}^+$ is $dx/x$ and that the scale invariance of…
Benford's law, or the law of the first significant digit, has been subjected to numerous studies due to its unique applications in financial fields, especially accounting and auditing. However, studies that addressed the law's establishment…
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 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 $[…
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…
In this paper, we will see that the proportion of d as leading digit, d $\in$ 1, 9, in data (obtained thanks to the hereunder developed model) is more likely to follow a law whose probability distribution is determined by a specific upper…
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…
According to Benford's Law, many data sets have a bias towards lower leading digits (about $30\%$ are $1$'s). The applications of Benford's Law vary: from detecting tax, voter and image fraud to determining the possibility of match-fixing…
In many real life situations, it is observed that the first digits (i.e., $1,2,\ldots,9$) of a numerical data-set, which is expressed using decimal system, do not follow a random distribution. Instead, smaller numbers are favoured by nature…
The so-called Benford's laws are of frequent use in order to observe anomalies and regularities in data sets, in particular, in election results and financial statements. Yet, basic financial market indices have not been much studied, if…
The Newcomb-Benford law, also known as the first-digit law, gives the probability distribution associated with the first digit of a dataset, so that, for example, the first significant digit has a probability of $30.1$ % of being $1$ and…
We discuss a common suspicion about reported financial data, in 10 industrial sectors of the 6 so called "main developing countries" over the time interval [2000-2014]. These data are examined through Benford's law first significant digit…
The Prime Numbers are well-known for their paradoxical stand regarding Benford's Law. On one hand they adamantly refuse to obey the law of Benford in the usual sense, namely that of a normal density of the proportion of primes with d as the…
According to Benford's law, the most significant digit in many datasets is not uniformly distributed, but obeys a well defined power law distribution with smaller digits appearing more often. Among one of the myriad particle physics…
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-…
Suppose that in a multiple choice examination the leading digit of the correct options follows Benford's Law, while the the leading digit of the distractors are uniform. Consider a strategy for guessing at answers that selects the option…
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…
Benford's Law states that the frequency of first digits of numbers in naturally occurring systems is not evenly distributed. Numbers beginning with a 1 occur roughly 30\% of the time, and are six times more common than numbers beginning…
Benford's law is the statement that in many real world data sets, the probability of having digit $d$ in base $B$ as the first digit is \log_{B}\!\left(\frac{d+1}{d}\right) for all $1 \leq d \leq B$. We sometimes refer to this as weak…
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…