Related papers: The Weibull Distribution and Benford's Law

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…

The diverse applications of the Benford law attract investigators working in various fields of physics, biology and sociology. At the same time, the groundings of the Benford law remain obscure. Our paper demonstrates that the Benford law…

We show the leading digits of a variety of systems satisfying certain conditions follow Benford's Law. For each system proving this involves two main ingredients. One is a structure theorem of the limiting distribution, specific to the…

The uneven distribution of digits in numerical data, known as Benford's law, was discovered in 1881. Since then, this law has been shown to be correct in copious numerical data relating to economics, physics and even prime numbers. Although…

Benford's law is an empirical law predicting the distribution of the first significant digits of numbers obtained from natural phenomena and mathematical tables. It has been found to be applicable for numbers coming from a plethora of…

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 is an empirical law which predicts the frequency of significant digits in databases corresponding to various phenomena, natural or artificial. Although counter intuitive at the first sight, it predicts a higher occurrence of…

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…

Benford's law predicts the occurrence of the $n^{\mathrm{th}}$ digit of numbers in datasets originating from various sources of the world, ranging from financial data to atomic spectra. It is intriguing that although many features of…

The reproducibility of academic research has long been a persistent issue, contradicting one of the fundamental principles of science. What is even more concerning is the increasing number of false claims found in academic manuscripts…

Feller's classic text 'An Introduction to Probability Theory and its Applications' contains a derivation of the well known significant-digit law called Benford's law. More specifically, Feller gives a sufficient condition ("large spread")…

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-…

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…

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 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 states that the occurrence of significant digits in many data sets is not uniform but tends to follow a logarithmic distribution such that the smaller digits appear as first significant digits more frequently than the larger…

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…

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…

Benford's law is an empirical ``law'' governing the frequency of leading digits in numerical data sets. Surprisingly, for mathematical sequences the predictions derived from it can be uncannily accurate. For example, among the first billion…

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…