Benfords Law or the First Digit Law - Essay Example

Benford’s Law or the First Digit Law History of Benford’s law Benford’s law or the first digit law states that the first digit in different types of data sets is usually distributed in a non-uniform manner. This law categorically states that number 1 will always appear as the first digit about 30$ of the time while number 2 will appear as the first digit about 18% of the time while number 9 will only appear first about 5% of the time. This law is applicable to various data sets such as street addresses, census data, stock prices as well as the lengths of rivers. Benford’s law was discovered back in 1881 by American astronomer names Simon Newcomb, who noticed that the earlier pages of logarithm tables that are used in the performance of calculations were much more worn that other pages. Newcomb published result become the first known instance of this observation and also includes the distribution on the second digit. He then proposed a law that is based on the probability of a single number N that is the first digit of a number was equal to log(N + 1) − log(N). The results from Benford’s law are used in different data such as street addresses, electricity bills, population numbers, lengths or rivers, stock prices, death rates, mathematical and physical constants as well as processes that are described using power law. The main condition for this law is that the data set or population must only consist of natural numbers (Nigrini 170). The results from the law tend to be highly accurate whenever the values are distributed across numerous orders of magnitude. How Benford’s law is used in acts fraud Benford’s law is also highly used in the detection of fraud, errors, embezzlements, and sloppy accountants. This is because those people who normally commit crime may end up creating fake payment amounts that may appear real. Benford’s law is a data mining approach that is used in auditing in order to examine the digit properties in different accounting data for the purposes of character identification. However, unless the person committing is aware of Benford’s law of distribution, then he will not be in a position to make up numbers that follow the proper curve and this makes it very easy to spot a potential fraud. People who commit crime also tend to distribute their digits in a fairly uniform manner. With a simple comparison of the frequency of the first digit from the data in accordance with the expected distributing according to Benford’s law will always reveal anomalous results. Based on this idea, Benford’s law could be used in auditing and forensic auditing to act as an indicator for expenses and accounting fraud. To use this law in detecting audit fraud, it is important for auditors to fully understand what it means by naturally occurring numbers or those numbers that do arise from real-life sources. Example of naturally occurring numbers includes chemical constants, death rates, population numbers, baseball statistics or even financial transitions. Benford’s law states that is there exists a set of naturally occurring numbers that are non-manipulated, and then the frequency of digits one to nine to occur must be expected. Because most of accounting and financial data do conform to the naturally occurring numbers, then auditors should be in a position to determine possible manipulations and irregularities in financial accounts. That is, since most accounting data conforms to the distribution of Benford’s law, then it will be appropriate for digital analysis of accounting data to be carried out using transactions that result from the combination of the digits (Nigrini 170). Accounting analysis using Benford’s law is more effective if the accounting items or transactions are analyzed as a whole instead of using sampling method. This is because the larger the data set, the more accurate is the analysis and the quicker it is to detect fraudulent activities. However, there are other counting data sets that do not conform to the distribution of Benford’s law. It is therefore important for auditors to decide and determine if the accounting date conforms to Benford’s distribution. Some accounting data may show flaws or operating inefficiencies in the system instead of showing fraud. Those accounts that have a built-in-maximum value will always not conform. Accounts that do not no conform make Benford analysis to be unlikely useful. In auditing, auditors should then perform further tests like the use of two digit test on all transactions that appear fraudulent and more so those transactions that have suspicious digit. Most business data such as expenses, sales numbers, disbursements, street addresses of the customers, and account receivables are naturally occurring numbers. If the auditors compare the frequency distribution of the first digit of the naturally occurring data with Benford’s law on expected distribution, then they will be in a position of spotting possible fraudulent transactions or errors (Nigrini 173). This means that is used correctly, then Benford’s law is an inexpensive and very useful tool in the identification of fraudulent and suspect accounts that require further auditing tests and analysis. Benford’s law therefore helps in predicting the percentage number of time that a number should appear in any number sequence. The application of Benford’s law in auditing therefore helps in making discoveries in terms of fraud or errors. Example of use Benford’s law in fraud detection Benford’s law is a statistical technique that is used in audit analytical procedures for determination of fraud. For example, assuming that an employee has been committing fraud through the creation and sending of fictitious payments to a vendor. The employee will be making up the amounts that are reflected in these fraudulent payments and so the numbers appearing will not be naturally occurring. Therefore, the leading digits of the valid transactions and the fictitious transactions will not follow Benford’s law. If those fraudulent payments have three as the leading digit like $39, $322 and $3, 187, then the performance of first-digit test using Benford’s law on the disbursement of data will enable the auditors to see that digit three has occurred more frequently than 12.5% which is the usual occurrence pattern hence a clear indication of fraud activities. Works Cited Mark, Nigrini. Benford's Law: Applications for Forensic Accounting, Auditing, and Fraud Detection. John Wiley & Sons, 2012, pg 170-175 Read More