Related papers: Quantitative Partition Models and Benford's Law
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 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 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…
Benford's law is an empirical edict stating that the lower digits appear more often than higher ones as the first few significant digits in statistics of natural phenomena and mathematical tables. A marked proportion of such analyses is…
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…
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…
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…
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…
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…
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,…
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…
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…
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…
A statistical model for the fragmentation of a conserved quantity is analyzed, using the principle of maximum entropy and the theory of partitions. Upper and lower bounds for the restricted partitioning problem are derived and applied to…
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 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…
A century ago, it was predicted that the first significant digit appearing in a data would be nonuniformly distributed, with the number one appearing with the highest frequency. This law goes by the name of Benford's law. It holds for data…
The occurrence of digits 1 through 9 as the leftmost nonzero digit of numbers from real-world sources is distributed unevenly according to an empirical law, known as Benford's law or the first digit law. It remains obscure why a variety of…
We develop two complementary generative mechanisms that explain when and why Benford's first-digit law arises. First, a probabilistic Turing machine (PTM) ensemble induces a geometric law for codelength. Maximizing its entropy under a…
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…