Managing Risk in Numbers Games

Benford's Law ◽  
2015 ◽  
Author(s):  
Mabel C. Chou ◽  
Qingxia Kong ◽  
Chung-Piaw Teo ◽  
Huan Zheng
Keyword(s):  
Empirical Data ◽  
Choice Model ◽  
Equal Probability ◽  
Benford’S Law ◽  
Benford's Law ◽  
Winning Number ◽  
Managing Risk ◽  
Numbers Games

This chapter applies Benford's law to study how players choose numbers in fixed-odds number lottery games. Empirical data suggests that not all players choose numbers with equal probability in lottery games. Some of them tend to bet on (smaller) numbers that are closely related to events around them (e.g., birthdays, anniversaries, addresses, etc.). In a fixed-odds lottery game, this small-number phenomenon imposes a serious risk on the game operator of a big payout if a very popular number is chosen as the winning number. The chapter quantifies this phenomenon and develops a choice model incorporating a modified Benford's law for lottery players to capture the magnitude of the small-number phenomenon observed in the empirical data.

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.

Scale-, Base-, and Sum-lnvariance

2015 ◽  
Author(s):  
Arno Berger ◽  
Theodore P. Hill
Keyword(s):  
Empirical Data ◽  
Scale Invariance ◽  
Benford’S Law ◽  
Invariance Property ◽  
Invariance Properties ◽  
Benford's Law ◽  
Base Invariance

This chapter establishes and illustrates three basic invariance properties of the Benford distribution that are instrumental in demonstrating whether or not certain datasets are Benford, and that also prove helpful for predicting which empirical data are likely to follow Benford's law closely. These are the scale-invariance property, base-invariance property, and sum-invariance property.

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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