Benford's Law Assignment Sample

Assignment
Benford's Law Being Applied to
A Hypothetical Situation
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TABLE OF CONTENTS
INTRODUCTION .......................................................................................................................... 4
AIM OF THE LAW........................................................................................................................ 6
CONCLUSION............................................................................................................................... 8
REFERENCES ............................................................................................................................... 9
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INTRODUCTION
As per as the topic is concern, the Benford’s law is the most appropriate law and logically
named as first-digit law by the mathematical experts. The law states that in most of the cases
when a number is derived, there are 30% of the chances that the number is 1 and it can be 9 only
with an approximately 4.6% times (Busta and Weinberg, 1998). The law is having the variant of
the both categories i.e. scale variant as well as base variant. Now as per the scale variant
approach is concern, if numbers of the list is multiplied by the one of the constant number and
then there won’t be any variation in the distribution of the list. The law is applicable in the areas
such as management of the stock prices, street address identification etc (Bierstaker, Brody and
Pacini, 2006). to some extent this is also used for the management of the census data and the
length of the rivers also.
The person named as Simon Newcomb was the one who invested this theory and later it
was named as Benford Law. This law was given importance by the physicist due to its nature
(Nigrini, 2012). the pure mathematical applicability is not possible in case of the this law and
therefore it was not granted as the part of pure mathematics (Nigrini, 2012). The determination
of the law is as follows:
Table 1: probability
(source : Benford’s law, 2001)

Figure 1: graph representing probability
(source : Benford’s law, 2001)
AIM OF THE LAW
The major aim of this law is to determine or identify the frauds. There are many
organizations where the people use to make some of the fake payments which are technically
assumed as real by nature (Hassan, 2003). But as soon as the auditor uses the Benford’s law
distribution, all the frauds that have been done are easily identified. The frauds are caught as the
curve that is displayed in an uneven manner and it becomes easy for the perpetrator to detect the
modification made by the users during payment and account management (Nigrini, 2012). As per
as the usefulness of the Benford’s law is concern, the table described below explains is as:-
Table 2: Use of the benford’s law analysis
USE OF THE BENFORD’S LAW ANALYSIS
1. When the set of the numbers are derived from a group of the numbers that are used in
combination.
2. In case of the transaction of data.
3. When a huge amount of the data are analyzed.
4. When the mean of the group of data appears to be higher than the median and the other
determined variables.
Some of the examples related to the above situation are as follows:-

applicability has been more practical then before (Coderre, 2009). The mathematical experts are
using this law in relation to the nature. This law has become an link between the mathematics
and nature (A Simple Explanation of Benford’s Law ). It has been seen that the counting is done
with the help of the numbers such as 1, 2, 3 whereas there counting done by the nature is done
with the help of the e0, ex, e2x, e3x, and so on.
Taking in to consideration there are some of the hypothetical situations where in actual
this law applicability would beneficial. As per the applicability of the Benford's law in real life, a
reseacher has collected all the data related to the economy of many countries (A Simple
Explanation of Benford’s Law). These data were analyzed by the application of this law. The
data were comprises of the economy of the countries that are using euro as the cvurrency for
transacvtion. During the analysis of the economic data of the countries, it was found that the
Greece is one of the country whose data are variating from the real variables. Due to the
implementation of the Benford's law, it was found that the data of the economy of Greece have
been manupulated as per the need (Aspectual Principle, Benford's Law and Russell's Paradox). It
was also indentified that the major reason behind the modification of the data was Maastricht
Treaty. As per this Greece will be the fully the member of the European Monetary Union. The
law was beneficial to understand the financial problems of the country Greece. Another example
opf the application of the Benford's law can be seen in case of the episode of 2006 of “The
Running Man” that is telecasted in the television as a crime drama numbers (Aspectual Principle,
Benford's Law and Russell's Paradox). With the help of this law, the character Charlie Eppes has
determined the variations in the burglaries of the season 2.
The formula that is used in case of Benford's law is as follows:
1
( ) = (1 + )
Here, d is a number 1,2,3 ans so on till 9.
P denotes the probability.
With the help of this formula the probability of the digit from 0 to 9 is determined as follows:-
Table 3: Probability of the digits as per law
(source: Nigrini, 1996)

The determination of the probability is done as:-
Table 4: Formula for the various digit
For the 1st
digit ( ) ( ( / ))
Here,
Here,
represents 1,2,3….9
For the 2nd
digit (
) ∑ ( ))
represents 1,2,3…0
For the two digit combinations = log(1 + (1/ ))
(
= 1 ) ( ( /
))/ ( )
Here, represents the 1st
digit
And the represents the 2 digit
nd
Along with the benefits there are some of the limitations associated with the law. This
law is not beneficial during the small samples. One of the example is the cheque of any of the
bank account for 20 times. The law can dtermine the number of the manupulations but the person
is not determined who has done all the manupulations.
CONCLUSION
As per the study of the Benford law is concern, it is determined as one of the major tool
for determining the suspect accounts that have the maximum number of the variations and along
with this these accounts can be used for investigating at the future prospects. There are many
softwares that are including this tool for the process of analysis. As per as the theory applicable,
the the mathematical and the nature relation could be determined due to it. This law is not onloy
beneficial for the intergration of the nature with mathematical application but is also beneficial
for the development of the practical appraoch of mathematics. The fraud that are being done on

REFERENCES
Journals
Busta, B. and Weinberg, R., 1998. "Using Benford’s law and neural networks as a review
procedure". Managerial Auditing Journal. 13(6). pp.356 – 366.
Bierstaker, L. J. Brody, G. R. and Pacini, C., 2006. Accountants' perceptions regarding fraud
detection and prevention methods, Managerial Auditing Journal, 21(5). pp.520 – 535.
Hassan, B., 2003. Examining data accuracy and authenticity with leading digit frequency
analysis. Industrial Management & Data Systems, 103(2). pp.121 – 125.
Books
Nigrini, M., 2012. Benford's Law: Applications for Forensic Accounting, Auditing, and Fraud
Detection Volume 586 of Wiley Corporate F&A. John Wiley & Sons.
Gonzalez-Garcia, J. and Pastor, C. G., 2009. Benford’s Law and Macroeconomic Data Quality .
International Monetary Fund.
Corazza, M. and Claudio, P., 2011. Mathematical and Statistical Methods for Actuarial Sciences
and Finance. Springer.
Nigrini, M., 2011. Forensic Analytics: Methods and Techniques for Forensic Accounting
Investigations. Wiley.
Miller, J. S. and Takloo-Bighash, R., 2006. An Invitation to Modern Number Theory, Volume 13.
Princeton University Press.
Brancik, K., 2012. Insider Computer Fraud: An In-depth Framework for Detecting and
Defending against Insider IT Attacks. CRC Press.
Coderre, D., 2009. Computer Aided Fraud Prevention and Detection: A Step by Step Guide. John
Wiley & Sons.
Online
A Simple Explanation of Benford’s Law., [Online]. Available through : <
http://test.stat.auckland.ac.nz/~fewster/RFewster_Benford.pdf>. [Accessed on 5
2013].
th
July
Aspectual Principle, Benford's Law and Russell's Paradox ., [Online]. Available through : <
http://arxiv.org/ftp/arxiv/papers/1012/1012.5537.pdf>. [Accessed on 5th
July 2013].

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