FIRST DIGIT DISTRIBUTION OF HADRON FULL WIDTH

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 distribution. We investigate, for the first time, the first digit distribution of the full widths of mesons and baryons in the well-defined science domain of particle physics systematically, and find that they agree excellently with the Benford distribution. We also discuss several general properties of Benford's law, i.e. the law is scale-invariant, base-invariant and power-invariant. This means that the lifetimes of hadrons also follow Benford's law.

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Composite Test inclusive of Benford’s Law, Noise reduction and 0-1 Test for effective detection of Chaos in Rotor-Stator Rub

10.21203/rs.3.rs-254264/v1 ◽

2021 ◽

Author(s):

Aman Kumar Srivast ◽

Mayank Tiwari ◽

Akhilendra Singh

Keyword(s):

Noise Reduction ◽

Dynamic Properties ◽

Signal To Noise Ratio ◽

Chaotic Signal ◽

Benford’S Law ◽

Noisy Environment ◽

Scale Invariant ◽

System A ◽

Benford's Law ◽

First Time

Abstract Segregating noise from chaos in a dynamical system has been one of the most challenging work for the researchers across the globe due to their seemingly similar statistical properties. Even the most used tools such as 0-1 test and Lyapunov exponents fail to distinguish chaos from regular dynamics when signal is mixed with noise. This paper addresses the issue of segregating the dynamics in a rotor-stator rub system when the vibrations are subjected to different levels of noise. First, the limitation of 0-1 test in segregating chaotic signal from regular signal mixed with noise has been established. Second, the underexplored Benford’s Law and its application to the vibratory dynamical rotor-stator rub system has been introduced for the first time. Using the Benford’s Law Compliance Test (BLCT), successful segregation of not only noise from chaos but also very low Signal to Noise Ratio (SNR) signals which are mainly stochastic has been achieved. The Euclidean Distance concept has been used to explore the scale-invariant probability distribution of systems that comply with Benford’s Law to separate chaos from noise. Moreover, for moderate bands of noise in signals, we have shown that the Schreiber’s Nonlinear Noise Reduction technique works effectively in reducing the noise without damaging the dynamic properties of the system. Combining these individual layers (0-1 Test, BLCT and Noise reduction) on a rotor system, a Decision Tree based method to effectively segregate regular dynamics from chaotic dynamics in noisy environment has been proposed.

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Introduction

An Introduction to Benford's Law ◽

10.23943/princeton/9780691163062.003.0001 ◽

2015 ◽

Cited By ~ 1

Author(s):

Arno Berger ◽

Theodore P. Hill

Keyword(s):

Numerical Data ◽

Benford’S Law ◽

Decimal Digit ◽

Mathematical Framework ◽

Benford's Law ◽

History Of ◽

Logarithmic Distribution ◽

Benford Law ◽

Special Case

This introductory chapter provides an overview of Benford' law. Benford's law, also known as the First-digit or Significant-digit law, is the empirical gem of statistical folklore that in many naturally occurring tables of numerical data, the significant digits are not uniformly distributed as might be expected, but instead follow a particular logarithmic distribution. In its most common formulation, the special case of the first significant (i.e., first non-zero) decimal digit, Benford's law asserts that the leading digit is not equally likely to be any one of the nine possible digits 1, 2, … , 9, but is 1 more than 30 percent of the time, and is 9 less than 5 percent of the time, with the probabilities decreasing monotonically in between. The remainder of the chapter covers the history of Benford' law, empirical evidence, early explanations and mathematical framework of Benford' law.

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LEI DE NEWCOMB BENFORD E AUDITORIA CONTÁBIL: UMA REVISÃO SISTEMÁTICA DE LITERATURA

Revista Gestão e Desenvolvimento ◽

10.25112/rgd.v17i2.2035 ◽

2020 ◽

Vol 17 (2) ◽

pp. 111

Author(s):

Caroline De Oliveira Orth ◽

Anna Tamires Michaelsen ◽

Arthur Frederico Lerner

Keyword(s):

Systematic Review ◽

Literature Review ◽

Corporate Finance ◽

Natural Number ◽

Benford’S Law ◽

Audit Tool ◽

Research Gaps ◽

Accounting Data ◽

Benford's Law ◽

Logarithmic Distribution

Lei de Newcomb Benford - LNB, foi concebida pelo astrônomo e matemático Simon Newcomb, em 1881. Seus estudos demonstraram que a ocorrência de um número natural, de modo espontâneo ou aleatório, não se dava na proporção esperada de 1/9, mas segundo uma distribuição logarítmica. Desde então, esta lei vem sendo testada em muitas áreas do conhecimento. Em finanças corporativas, os estudiosos têm testado a lei para investigar fraudes em dados contábeis. Contudo, ainda não há consenso sobre a eficácia da LNB nesse âmbito. Assim, o objetivo deste artigo é identificar os argumentos favoráveis e contrários, bem como os métodos de pesquisa e os principais achados das pesquisas sobre a aplicação da LNB como ferramenta de auditoria. Para tanto, aplicou-se uma Revisão Sistemática de Literatura, seguindo os passos de Levy e Ellis (2006). Deste modo, além de informações sobre autoria, modelos utilizados pelos autores para suportar suas conclusões e seus principais achados, apresentam-se lacunas de pesquisa, e as implicações para o futuro da pesquisa são discutidas.Palavras-chave: Lei de Newcomb Benford. Revisão sistemática. Auditoria contábil.ABSTRACTNewcomb Benford’s Law - LNB, was conceived by the astronomer and mathematician Simon Newcomb, in 1881. His studies showed that the occurrence of a natural number, spontaneously or randomly, did not occur in the expected proportion of 1/9, but according to a logarithmic distribution. Since then, this law has been tested in many areas of knowledge. In corporate finance, scholars have tested the law to investigate fraud in accounting data. However, there is still no consensus on the effectiveness of LNB in this area. Thus, the objective of this article is to identify the arguments for and against, as well as the research methods and the main findings of research on the application of LNB as an audit tool. For that, a Systematic Literature Review was applied, following the steps of Levy and Ellis (2006). Thus, in addition to information on authorship, models used by the authors to support their conclusions and main findings, research gaps are presented, and the implications for the future of research are discussed.Keywords: Newcomb Benford’s law. Systematic review. Accounting audit..

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Benfordʼs Law in the Natural Sciences

Benford's Law ◽

10.23943/princeton/9780691147611.003.0016 ◽

2015 ◽

Author(s):

David Hoyle

Keyword(s):

Scale Invariance ◽

Natural Sciences ◽

Scientific Data ◽

Benford’S Law ◽

Reasonable Assumption ◽

Data Sets ◽

Scale Invariant ◽

Data Set ◽

Benford's Law ◽

Potential Applications

This chapter focuses on the occurrence of Benford's law within the natural sciences, emphasizing that Benford's law is to be expected within many scientific data sets. This is a consequence of the reasonable assumption that a particular scientific process is scale invariant, or nearly scale invariant. The chapter reviews previous work from many fields showing a number of data sets that conform to Benford's law. In each case the underlying scale invariance, or mechanism that leads to scale invariance, is identified. Having established that Benford's law is to be expected for many data sets in the natural sciences, the second half of the chapter highlights generic potential applications of Benford's law. Finally, direct applications of Benford's law are highlighted, whereby the Benford distribution is used in a constructive way rather than simply assessing an already existing data set.

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On the significands of uniform random variables

Journal of Applied Probability ◽

10.1017/jpr.2018.23 ◽

2018 ◽

Vol 55 (2) ◽

pp. 353-367 ◽

Cited By ~ 2

Author(s):

Arno Berger ◽

Isaac Twelves

Keyword(s):

Random Variables ◽

Random Variable ◽

Benford’S Law ◽

Elementary Calculation ◽

Sharp Bounds ◽

Large Spread ◽

Benford's Law ◽

Logarithmic Distribution

Abstract For all α > 0 and real random variables X, we establish sharp bounds for the smallest and the largest deviation of αX from the logarithmic distribution also known as Benford's law. In the case of uniform X, the value of the smallest possible deviation is determined explicitly. Our elementary calculation puts into perspective the recurring claims that a random variable conforms to Benford's law, at least approximately, whenever it has large spread.

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A Short Introduction to the Mathematical Theory of Benfordʼs Law

Benford's Law ◽

10.23943/princeton/9780691147611.003.0002 ◽

2015 ◽

Author(s):

Arno Berger ◽

T. P. Hill

Keyword(s):

Mathematical Theory ◽

Real Life ◽

Random Processes ◽

Basic Theory ◽

Benford’S Law ◽

Data Sets ◽

Life Data ◽

Real Life Data ◽

Benford's Law ◽

Logarithmic Distribution

This chapter embarks on a brief discussion of the mathematical theory of Benford's law. This law is the observation that in many collections of numbers, be they mathematical tables, real-life data, or combinations thereof, the leading significant digits are not uniformly distributed, as might be expected, but are heavily skewed toward the smaller digits. More specifically, Benford's law states that the significant digits in many data sets follow a very particular logarithmic distribution. The chapter lays out the basic theory of Benford's law before highlighting its more specific components: the significant digits and the significand (function), as well as the Benford property and its four characterizations. Finally, the chapter presents the basic theory of Benford's law in the context of deterministic and random processes.

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