Related papers: Double-Crossing Benford's Law
Benford's law is frequently used to evaluate the likihood that data is misrepresentative. Typically statistical tests measure the likihood. Another method of employing Benford's law is to compare the frequency of leading digits to the…
Nature and our world have a bias! Roughly $30\%$ of the time the number $1$ occurs as the leading digit in many datasets base $10$. This phenomenon is known as Benford's law and it arrises in diverse fields such as the stock market,…
Many systems exhibit a digit bias. For example, the first digit base 10 of the Fibonacci numbers, or of $2^n$, equals 1 not 10% or 11% of the time, as one would expect if all digits were equally likely, but about 30% of the time. This…
We address the task of identifying anomalous observations by analyzing digits under the lens of Benford's law. Motivated by the crucial objective of providing reliable statistical analysis of customs declarations, we answer one major and…
The goal of this note is to show that a widespread claim about Benford's Law, namely, that the range of every Benford distribution spans at least several orders of magnitude, is false. The proof is constructive and concrete examples are…
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…
Benford's Law describes the finding that the distribution of leading (or leftmost) digits of innumerable datasets follows a well-defined logarithmic trend, rather than an intuitive uniformity. In practice this means that the most common…
Benford's law states that in data sets from different phenomena leading digits tend to be distributed logarithmically such that the numbers beginning with smaller digits occur more often than those with larger ones. Particularly, the law is…
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…
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 describes the distribution of the first digit of numbers appearing in a wide variety of numerical data, including tax records, and election outcomes, and has been used to raise "red flags" about potential anomalies in the data…
Benford's law states that many data sets have a bias towards lower leading digits (about $30\%$ are 1s). There are numerous applications, from designing efficient computers to detecting tax, voter and image fraud. It's important to know…
The Newcomb-Benford Law, which is also called the first digit phenomenon, has applications in diverse phenomena ranging from social and computer networks, engineering systems, natural sciences, and accounting. In forensics, it has been used…
Many mathematical, man-made and natural systems exhibit a leading-digit bias, where a first digit (base 10) of 1 occurs not 11\% of the time, as one would expect if all digits were equally likely, but rather 30\%. This phenomenon is known…
The probability that a number in many naturally occurring tables of numerical data has first significant digit $d$ is predicted by Benford's Law ${\rm Prob} (d) = \log_{10} (1 + {\displaystyle{1\over d}}), d = 1, 2 >..., 9$. Illustrations…
This article presents a concise proof of the famous Benford's law when the distribution has a Riemann integrable probability density function and provides a criterion to judge whether a distribution obeys the law. The proof is intuitive and…
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…
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…
Benford's law is the statement that in many real-world data sets, the probability of having digit \(d\) in base \(B\), where \(1 \leq d \leq B\), as the first digit is \(\log_{B}\left(\tfrac{d+1}{d}\right)\). We sometimes refer to this as…
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…