Related papers: Benford distributions in NMR
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.
The neuromuscular junction represents a relevant substrate for revealing important biophysical mechanisms of synaptic transmission. In this context, calcium ions are important in the synapse machinery, providing the nervous impulse…
We check if the first significant digit of the dispersion measure of pulsars and Fast Radio Bursts (using the CHIME catalog) is consistent with the Benford distribution. We find a large disagreement with Benford's law with $\chi^2$ close to…
The first digit (FD) phenomenon i.e., the significant digits of numbers in large data are often distributed according to a logarithmically decreasing function was first reported by S. Newcomb and then many decades later independently by F.…
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…
In this paper, we develop a framework of 'Benford models' for counter-intelligence investigations which analyze frequency data of a suspect's visits to physical locations, online websites, and communication channels. We accomplish this by…
The invariance of Benford-Newcomb law under base changing is employed to test whether or not some data follow such distribution. Taking into account the Brazilian senate election in 1994, changes in the numerical base were able to evidence…
Statistical characteristics of network traffic have attracted a significant amount of research for automated network intrusion detection, some of which looked at applications of natural statistical laws such as Zipf's law, Benford's law and…
A beautiful theorem of Zeckendorf states that every integer can be written uniquely as the sum of non-consecutive Fibonacci numbers $\{ F_i \}_{i = 1}^{\infty}$. A set $S \subset \mathbb{Z}$ is said to satisfy Benford's law if the density…
The yearly aggregated tax income data of all, more than 8000, Italian municipalities are analyzed for a period of five years, from 2007 to 2011, to search for conformity or not with Benford's law, a counter-intuitive phenomenon observed in…
In this paper, we present a possible theoretical explanation for benford's law. We develop a recursive relation between the probabilities, using simple intuitive ideas. We first use numerical solutions of this recursion and verify that the…
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…
We explore the possibility of using machine learning to identify interesting mathematical structures by using certain quantities that serve as fingerprints. In particular, we extract features from integer sequences using two empirical laws:…
We discuss various statistical distributions of earthquake numbers. Previously we derived several discrete distributions to describe earthquake numbers for the branching model of earthquake occurrence: these distributions are the Poisson,…
We examine the relationship between two different types of ranked data, frequencies and magnitudes. We consider data that can be sorted out either way, through numbers of occurrences or size of the measures, as it is the case, say, of moon…
Benford's law is often used as a support to critical decisions related to data quality or the presence of data manipulations or even fraud. However, many authors argue that conventional statistical tests will reject the null of data…
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…
In relation to recent experimental data [1], we develop a theory framework for demonstrating the feasibility of detecting sharp Nuclear Magnetic Resonance (NMR) oscillations in a real time ESR data. The procedure is to follow real time…
We study the individual digits for the absolute value of the characteristic polynomial for the Circular $\beta$-Ensemble. We show that, in the large $N$ limit, the first digits obey Benford's Law and the further digits become uniformly…
Ultralow-field nuclear magnetic resonance (NMR) provides a new regime for many applications ranging from materials science to fundamental physics. However, the experimentally observed spectra show asymmetric amplitudes, differing greatly…