相关论文: Citations to articles citing Benford's law: a Benf…
Iafrate, Miller, and Strauch [Equipartition and a Distribution for Numbers: A Statistical Model for Benford's Law," arXiv:1503.08259] construct and test a statistical model for partitioning a conserved quantity. One consequence of their…
We provide general expressions for the joint distributions of the $k$ most significant $b$-ary digits and of the $k$ leading continued fraction coefficients of outcomes of an arbitrary continuous random variable. Our analysis highlights the…
For the first time, we introduce "Scaling invariable Benford distance" and "Benford cyclic graph", which can be used to analyze any data set. Using the quantity and the graph, we analyze some date sets with common distributions, such as…
Academic papers have been the protagonists in disseminating expertise. Naturally, paper citation pattern analysis is an efficient and essential way of investigating the knowledge structure of science and technology. For decades, it has been…
We study the fame distribution of scientists and other social groups as measured by the number of Google hits garnered by individuals in the population. Past studies have found that the fame distribution decays either in power-law…
Numerical data for the distribution of citations are examined for: (i) papers published in 1981 in journals which are catalogued by the Institute for Scientific Information (783,339 papers) and (ii) 20 years of publications in Physical…
Gradually Truncated Power law distribution - Citation of scientists Hari M. Gupta, Jose R. Campanha and Bianca A. Ferrari Unesp - Physics Dpto. - Rio Claro Sao Paulo - Brazil Abstract The number of times, a scientist is cited in other…
This paper explores a real-world fundamental theme under a data science perspective. It specifically discusses whether fraud or manipulation can be observed in and from municipality income tax size distributions, through their aggregation…
We present empirical data on frequency and pattern of misprints in citations to twelve high-profile papers. We find that the distribution of misprints, ranked by frequency of their repetition, follows Zipf's law. We propose a stochastic…
This article presents a modern deterministic framework for the study of leading significant digit distributions in numerical data. Rather than relying on traditional probabilistic or mixture-based explanations, we demonstrate that the…
Understanding the statistical laws governing citation dynamics remains a fundamental challenge in network theory and the science of science. Citation networks typically exhibit in-degree distributions well approximated by log-normal…
Statistical analysis of repeat misprints in scientific citations leads to the conclusion that about 80% of scientific citations are copied from the lists of references used in othe papers. Based on this finding a mathematical theory of…
The distribution of numbers in human documents is determined by a variety of diverse natural and human factors, whose relative significance can be evaluated by studying the numbers' frequency of occurrence. Although it has been studied…
This paper proposes a novel approach for statistical modelling of a continuous random variable $X$ on $[0, 1)$, based on its digit representation $X=.X_1X_2\ldots$. In general, $X$ can be coupled with a latent random variable $N$ so that…
It is pointed out that the language of quotient groups and wrapped distributions allows an elementary discussion of Benford's Law, and adds arguments supporting wide-spread observability of this statistics.
Changes in citation distributions over 100 years can reveal much about the evolution of the scientific communities or disciplines. The prevalence of uncited papers or of highly-cited papers, with respect to the bulk of publications,…
A study released by the Google Scholar team found an apparently increasing fraction of citations to old articles from studies published in the last 24 years (1990-2013). To demonstrate this finding we conducted a complementary study using a…
Let $f(z)=\sum_{n=1}^\infty \lambda_f(n)e^{2\pi i n z}\in S_{k}^{new}(\Gamma_0(N))$ be a normalized Hecke eigenform of even weight $k\geq2$ on $\Gamma_0(N)$ without complex multiplication. Let $\mathbb{P}$ denote the set of all primes. We…
Power laws are a characteristic distribution that are ubiquitous, in that they are found almost everywhere, in both natural as well as in man-made systems. They tend to emerge in large, connected and self-organizing systems, for example,…
Three influential laws, namely Sarnoff's Law, Metcalfe's Law, and Reed's Law, have been established to describe network value in terms of the number of neighbors, edges, and subgraphs. Here, we highlight the coexistence of these laws in…