Related papers: Benford-Newcomb Subsequences for Fraud Detection
It is known that if X is uniformly distributed modulo 1 and Y is an arbitrary random variable independent of X then Y+X is also uniformly distributed modulo 1. We prove a converse for any continuous random variable Y (or a reasonable…
Internet research on search engine quality and validity of results demand much concern. Thus, the focus in our study has been to measure the impact of quotation marks usage on the internet search outputs in terms of google search outcomes…
We give an algorithm A which assigns probabilities to logical sentences. For any simple infinite sequence of sentences whose truth-values appear indistinguishable from a biased coin that outputs "true" with probability p, we have that the…
Suppose you look at today's stock prices and bet on the value of the first digit. One could guess that a fair bet should correspond to the frequency of $1/9 = 11.11%$ for each digit from 1 to 9. This is by no means the case, and one can…
A random variable X that is base b Benford will not in general be base c Benford when c is not equal to b. This paper builds on two of my earlier papers and is an attempt to cast some light on the issue of base dependence. Following some…
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…
Rule based classifiers that use the presence and absence of key sub-strings to make classification decisions have a natural mechanism for quantifying the uncertainty of their precision. For a binary classifier, the key insight is to treat…
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…
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…
Among econophysics investigations, studies of religious groups have been of interest. On one hand, the present paper concerns the Antoinist community financial reports, - a community which appeared at the end of the 19-th century in…
We demonstrate that large texts, representing human (English, Russian, Ukrainian) and artificial (C++, Java) languages, display quantitative patterns characterized by the Benford-like and Zipf laws. The frequency of a word following the…
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…
This paper has several major purposes. The central purpose is to describe the "Benford analysis" of a positive random variable and to summarize some results from investigations into base dependence of Benford random variables. The principal…
We propose a new method based on machine learning to \emph{play the devil's advocate} and investigate the impact of unknown systematic effects in a quantitative way. This method proceeds by reversing the measurement process and using the…
An important aspect of religious association is that adherents, as part of their religious duty, carry out various activities. One religious group known for keeping the elaborate records of day-to-day activities of its members is the…
For arbitrary Borel probability measures with compact support on the real line, characterizations are established of the best finitely supported approximations, relative to three familiar probability metrics (Levy, Kantorovich, and…
Statistical divergence is widely applied in multimedia processing, basically due to regularity and interpretable features displayed in data. However, in a broader range of data realm, these advantages may no longer be feasible, and…
In this paper, a new method of detection of election fraud is proposed. This method is based on the calculation of the ratio of two standard normal random variables; estimation of parameters of obtained sample and comparison of these…
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…
Using the sum invariance property of Benford random variables, we prove that an $n$-digit Benford variable converges to a Benford variable as $n$ approaches infinity.