相关论文: A concise proof of Benford's law

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, 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…

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…

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…

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…

A simple fragmentation model is introduced and analysed. We show that, under very general conditions, an effective power law for the mass distribution arises with realistic exponent. This exponent has a universal limit, but in practice the…

In this paper, we will see that the proportion of d as p th digit, where p > 1 and d $\in$ 0, 9, in data (obtained thanks to the hereunder developed model) is more likely to follow a law whose probability distribution is determined by a…

A phenomenological law, called Benford's law, states that the occurrence of the first digit, i.e., $1,2,...,9$, of numbers from many real world sources is not uniformly distributed, but instead favors smaller ones according to a logarithmic…

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…

A sequence of real numbers (x_n) is Benford if the significands, i.e. the fraction parts in the floating-point representation of (x_n) are distributed logarithmically. Similarly, a discrete-time irreducible and aperiodic finite-state Markov…

We provide conditions on dependent and on non-stationary random variables $X_n$ ensuring that the mantissa of the sequence of products $\left(\prod_{1}^{n}X_k\right)$ is almost surely distributed following the Benford's law or converges in…

It is known that increasing powers of a continuous random variable converge in distribution to Benford's law as the exponent approaches infinity. The rate of convergence has been estimated using Fourier analysis, but we present an…

Benford's Law (BL) or the Significant Digit Law defines the probability distribution of the first digit of numerical values in a data sample. This Law is observed in many naturally occurring datasets. It can be seen as a measure of…

A recent article by Alexopoulos and Leontsinis presented empirical evidence that the first digits of the distances to galaxies are a reasonably good fit to the probabilities predicted by Benford's law, the well known logarithmic statistical…

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…

There are two fair ways to distribute particles in boxes. The first way is to divide the particles equally between the boxes. The second way, which is calculated here, is to score fairly the particles between the boxes. The obtained power…

There are now many theoretical explanations for why Benford's law of digit bias surfaces in so many diverse fields and data sets. After briefly reviewing some of these, we discuss in depth recurrence relations. As these are discrete…

In this work, we prove the joint convergence in distribution of $q$ variables modulo one obtained as partial sums of a sequence of i.i.d. square integrable random variables multiplied by a common factor given by some function of an…

Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…

The phenomenon of superconvergence is proved for all freely infinitely divisible distributions. Precisely, suppose that the partial sums of a sequence of free identically distributed, infinitesimal random variables converge in distribution…