Several common probability distributions obey Benford’s law

2020 ◽  
Vol 540 ◽  
pp. 123129
Author(s):  
Guojun Fang ◽  
Qihong Chen
Keyword(s):  
Probability Distributions ◽  
Benford’S Law ◽  
Benford's Law ◽  
Common Probability

Benfordʼs Law Geometry

Benford's Law ◽  
2015 ◽  
Author(s):  
Lawrence Leemis
Keyword(s):  
Empirical Data ◽  
Probability Distributions ◽  
Benford’S Law ◽  
Data Sets ◽  
Normal Distributions ◽  
Benford's Law ◽  
Using Data

This chapter switches from the traditional analysis of Benford's law using data sets to a search for probability distributions that obey Benford's law. It begins by briefly discussing the origins of Benford's law through the independent efforts of Simon Newcomb (1835–1909) and Frank Benford, Jr. (1883–1948), both of whom made their discoveries through empirical data. Although Benford's law applies to a wide variety of data sets, none of the popular parametric distributions, such as the exponential and normal distributions, agree exactly with Benford's law. The chapter thus highlights the failures of several of these well-known probability distributions in conforming to Benford's law, considers what types of probability distributions might produce data that obey Benford's law, and looks at some of the geometry associated with these probability distributions.

The Benford Property

2015 ◽  
Author(s):  
Arno Berger ◽  
Theodore P. Hill
Keyword(s):  
Probability Distributions ◽  
Random Variables ◽  
Benford’S Law ◽  
Real Numbers ◽  
Benford's Law

In order to translate the informal versions of Benford's law into more precise formal statements, it is necessary to specify exactly what the Benford property means in various mathematical contexts. For the purpose of this book, the objects of interest fall mainly into three categories: sequences of real numbers, real-valued functions defined on [0,+ ∞), and probability distributions and random variables. This chapter defines Benford sequences, functions, and random variables, with examples of each.

scholarly journals Reliability of Financial Information from the Perspective of Benford’s Law

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 557
Author(s):  
Ionel Jianu ◽  
Iulia Jianu
Keyword(s):  
Financial Reporting ◽  
Capital Market ◽  
Financial Statements ◽  
Financial Information ◽  
Benford’S Law ◽  
Professional Judgment ◽  
Reporting Standards ◽  
Financial Reporting Standards ◽  
Benford's Law ◽  
Before And After

This study investigates the conformity to Benford’s Law of the information disclosed in financial statements. Using the first digit test of Benford’s Law, the study analyses the reliability of financial information provided by listed companies on an emerging capital market before and after the implementation of International Financial Reporting Standards (IFRS). The results of the study confirm the increase of reliability on the information disclosed in the financial statements after IFRS implementation. The study contributes to the existing literature by bringing new insights into the types of financial information that do not comply with Benford’s Law such as the amounts determined by estimates or by applying professional judgment.

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