Free Essay

Benford's Law

In: Business and Management

Submitted By jla6x7
Words 1247
Pages 5
Mark Nigrini – Benford’s Law

After attending Mark’s presentation, I feel as though I have a better understanding of Benford’s

law. Mark talked about the history of Benford’s law and how Frank had tested it and first used it as

physicist. He showed us several graphs of data where Benford’s law applied. Not only did it apply to

financial data, but it also applies to many other sets of data. I was extremely fascinated when he showed

us a graph that compared the speed of river currents to Benford’s law. It truly made me believe and

understand that sets of data, when compared on a large scale, should follow Benford’s law. If they don’t

follow Benford’s law, then it is highly likely that something isn’t being allowed to happen naturally.

Mark explained to us that the first digit is the only digit that should be affected by the higher

probability of it being 1, 2, or 3. The possibility that the first digit of a set of numbers that should follow

Benford’s law is 1, 2, or 3 is approximately 60%. 30% of the 60% is just for the probability of the first

number being 1. Because only the first number should be affected by a higher percentage of 1, 2 or 3,

this means that the ending numbers should be evenly spread percentage wide. You should be alarmed if

you see any significant spikes in data for the ending digits. This may mean that the numbers are being

Spikes in graphs may be explained by artificial alterations or things like rounded numbers. There

may be fixed numbers that always turn out to be rounded numbers. Let’s say for example that you

receive a bill every month from your internet provider. It is highly unlikely that your bill would vary from

month to month. You would more than likely have a fixed cost that is set at a rounded number. It

wouldn’t be a red flag to see a cost for $2,500 every month for your business to pay for its internet. This

may cause a set of data to not obey Benford’s law. You may be looking at a set of data and thinking,

“Wow, something is seriously wrong here.” As soon as you dig into the data, you should be able to

identify the things that make the graph not obey Benford’s Law.

It isn’t uncommon for fraudsters to hang around specific thresholds that they fear may trigger

extra attention to the crimes they are committing. After fraud has been committed over a long period of

time, if Benford’s law is applied to the data, you will notice that the 9’s and 0’s may appear far more

often than other numbers. This is because fraudsters may be trying to stay under or over a specific

number that may grab someone’s attention to what is happening. If you notice huge spikes in these

threshold numbers, it may be a good sign that there is a fraudster amongst your company.

He also spoke with us about the irony of how we are taught accounting as students. There have

been tests through a large variety of accounting text books. The top numbers used in the books are all

rounded numbers. He talked with us about the irony on how we are constantly being shown rounded

numbers in our textbooks but how we are supposed to label them as red flags in the professional world.

It would be alarming if we constantly saw rounded number’s in our company’s accounting books, then

why are we being constantly fed those numbers in our text books?

Mark also told us about a couple crimes that had occurred recently. He explained that if

Benford’s law would’ve been applied they may have been caught sooner. It also appeared that there

was an extremely severe lack in controls in general. Both crimes’ involved persons who had to create

their unique number to receive as payment. This means the numbers they were generating were not

Darlene Wooten and Charlene Corley were twin sisters that owned a hardware company. They

would get contracts with the department of defense and sell them small amounts of goods. However,

they noticed something very strange. No matter the amount, the department of defense would almost

always pay for whatever the shipping cost turned out to be. At first, the sisters would set a shipping cost

that matched the price of the invoice. Then, they would slowly start to double the cost. After years

passed, they were charging $30,000 shipping for a $30 product. They would continue to receive

approvals and payments for the invoices that they sent. They continued to increase the shipping costs to

an amazing amount of money. At one point, they were charging over $900,000 in shipping for an item

that was under $5. The sisters had racked up over $20 million in revenue from the department of

defense. They had bought and excessive amount of cars, houses, and others goods. The eventually got

caught when they mistakenly created two invoices using the same number. Mark seems to think the

only reason they were caught was because after this duplicate number, the invoice was actually

physically placed on someone’s desk rather than being sent through their automatic system. Anyone

would notice an issue with a $1 invoice that included a $900,000 shipping cost. After getting caught, one

of the sisters committed suicide. The other sister blamed all the wrongdoing on the deceased. She was

sentenced to 6 years in jail and owed $15 million in restitution. The joke of the whole story is that she

only has to pay back the $15 million in amounts of $300 a month. AKFJHSKJFHKSSDHGKJSDHGKJSDH!!!!

Is that what you were thinking too? That means after 50,000 months of $300 payments, her restitution

would finally be paid off. If you guessed that that was equivalent to 4,166 years, you were right.

Mark also talked with us about Harriette Walters. She fraudulently gave away over $31 million in

tax refunds to family and friends. In doing so, she was most definitely able to get a significant portion for

herself for the amount given away. If the tax refunds were properly audited, someone would have been

able to spot the errors in the amounts allotted for the refunds. Some of the amounts refunded were

perfectly rounded numbers. Since there is a specific calculation used to calculate tax refunds, this makes

perfectly rounded numbers impossible. She was clearly just making up her own numbers to reward

friends and family. She eventually got caught when she forged an official’s signature and sent it in the

mail in attempt to convince a bank that a refund given to a family member of hers was legitimate.

However, they were already concerned because the $400,000 check was attempting to be cashed at a

bank that was located inside a convenient store. They don’t often see deposits for that amount, and

when they do, you can be assured that will be asking questions.

After listening to Mark, I feel as though I am a lot more in tune with Benford’s Law. He was able

to provide his own examples of different sets of data that he tested against Benford’s Law. It was

amazing to see the graph line up perfectly with the statistics and probabilities that are stated in

Benford’s Law. I am more than interested in doing my own research and tests using Benford’s Law and

Similar Documents

Free Essay


...2501 Project Benford’s and Zipf’s Law Abstract Both Benford’s and Zipf’s Law are the result from a lot of real life data, and they are relative and can be applied in our real life. This paper will introduce and explain these two laws in a simply way. Benford’s Law Benford's Law, also called the First-Digit Law, refers to the frequency distribution of digits in many (but not all) real-life sources of data. In this distribution, 1 occurs as the leading digit about 30% of the time, while larger digits occur in that position less frequently: 9 as the first digit less than 5% of the time. Benford's Law also concerns the expected distribution for digits beyond the first, which approach a uniform distribution. For , the proportion of whose first digit is is approximately . Thus, for instance, should have a first digit of 1 about 30% of the time, but a first digit of 9 only about 5% of the time. The American astronomer Simon Newcomb discovered the law in 1881 that noticed that the first pages of books of logarithms were soiled much more than the remaining pages. In 1938, Frank Benford arrived at the same formula after a comprehensive investigation of listings of data covering a variety of natural phenomena. The law applies to budget, income tax or population figures as well as street addresses of people listed in the book American Men of Science. In the face of such universality of the law, it's quite astonishing that there exists a more general framework - Zipf's Law. Which, in......

Words: 919 - Pages: 4

Premium Essay

Forensic Accounting

...combat organized crime, forbids certain organized gambling, and to allow the prosecution of criminal leaders who may not have been directly involved in a series of criminal acts but whose criminal organization carried out the details. 2. Benford’s Law (1)定义:A fraud indicator that predicts the relative incidence of first digits of numbers in certain types of random data. (2)Benford Analysis Benford analysis presents another interesting approach to fraud detection. Its general use is to determine the likelihood that fraud exists in records. This technique is based on Benford’s law, named after Frank Benford who realized that the likelihood that numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 will appear as the first digit in numbers occurring in a random data set conforms to a predictable pattern. That is, the number 1 is more likely to appear as the first digit in a number than is the number 2. The pattern of likelihood (Figure 6.6) continues with other digits: The number 2 is more likely to appear as a first digit than 3, 3 is more likely to appear as a first digit than 4, and so on. Note that just because the likelihood is higher that 7 will appear as a first digit than will 8 does not mean that a number that begins with 8 is due to fraud. Benford’s law can be used to determine whether a higher risk than normal exists that a population of numbers—for example, a collection of vendor’s invoices—contain fraud. Specifically, the invoice amounts can be...

Words: 5213 - Pages: 21

Premium Essay

Red Light

...cameras in the law. Nearly everyone else, not so much. Why? Is Florida a hotbed of red light runners crashing into others? If you look at our traffic crash data over the past several years, you'll see that is not the case. My background is law enforcement. I worked for two years as a Florida deputy sheriff and the remaining 23 years of my 25-year career with the Florida Highway Patrol, where I worked as a trooper, traffic homicide investigator, and squad sergeant, and retired as an investigations lieutenant. I currently operate a small lobbying firm in Tallahassee that specializes in issues involving liberty. According to our Department of Highway Safety, red light running as a cause is around 2 to 3 percent of all crashes. One thing you will never see in any news story about the devices is how many red light running crashes are taking place to justify the need for these automated for-profit law enforcement devices. (Like the Florida Legislature, I don't call them red light cameras either.) Why didn't the Legislature call them red light cameras? It is simple really. Running a red light is a traffic infraction, as is speeding and passing a stopped school bus. It just so happens one automated for-profit company has devices for these other infractions. Calling the devices red light cameras would limit their use. Calling them traffic infraction detectors means they can enforce all of these laws and any other infractions. Why do I call them automated for-profit law......

Words: 2476 - Pages: 10

Premium Essay

Gun Laws

...not have them. Some believe that guns kill people. Some believe that there should be strict control on guns. What do you believe? I personally believe that yes there should be some restrictions on gun control but not as much as the government wants us to have. Guns should be restricted from those who have mental disorders, guns should be restricted from those whom also have violent criminal offenses behind them. Guns should not be made hard for law abiding legal citizens to acquire. There should not be strict rules on clip size. If there is a restriction on clip size what happens when a criminal attacks and has a large clip size and you don’t because you follow the law and they don’t. Guns may not be banned from sale they might not be impossible to get but the government is making it harder for us to get them. The right to bear arms is our right and It should not be possible to change that or take it away. Some conspiracies say that all of these shootings are staged. A lot of people believe that is was a act to help pass gun laws performed by paid actors. There are pictures showing how some of these people are connected from incident to incident. Should these conspiracies be believed or just passed off as another myth and not given a chance. In fact the more gun shootings there are the worse it looks for Obamas plan to pass. I think that people feel they need their guns in order to protect...

Words: 270 - Pages: 2

Free Essay


...whereas others are of the idea that we should be given our own freedom to be able to say anything we want to. In my country, Kuwait the government has assumed control over the media through many censures of magazines, movies and programs aired in television. Though the constitution guarantees for freedom, but only under the confines of the law, it seems contradictory. There are various sources that shed light in this issue of government control in my country. We are going to look at three of them; the world press freedom review, the Amman j blog and the spokesman review. Many newspapers are individually owned, and though this maybe the situation which would allow for any kind of expressions of opinions, the newspapers are restricted to speaking against the government or the Islamic religion to some degree. There is an instance where according to a report, from the world press freedom, that a certain publication was viewed as offering support to Iraq and was banned in the country(2002). This scenario is similar to others going to be discussed because they are all based on the press laws that ban the country’s media from going against some of the laws that are laid out by the government. Defaming the country’s religion is not acceptable according to the government. Though the government is under the constitution, the...

Words: 682 - Pages: 3

Premium Essay


...parties must have judgment or discernment, must be able to understand the nature of the act and its consequences. A pers that has a full concrete capacity is presumed by law to have judgment or discernment. This legal presumption may be overruled by proving the temporary lack of judgment of the person in question, as for example for temporarily mental illness, or influence of drugs. You can find this in the civil code Art. 1205 paragraph 1 2. To be expressed by a pers. who has the intention to produce legal effects. This condition is not fulfilled when for example the pers. Is only kidding, he has no real intention to conclude a contract – informal bet. 3. To be externalized. It means that the consent must result from the words or even the actions of the parties. In this respect several problems arise in case of silence. Generally in our law the consent cannot be implied and therefore in case of silence it is considered that there is no consent at all. The inaction of the parties or the silence is not conceived as an expression of the intention to conclude a contract. However there are some exceptions to this rule, as follows (Art 1196 – paragraph 2) Exceptions: * The law expressly provides that in some cases that the silence of one of the parties must be considered as consent. For eg according the law the rent contract...

Words: 1260 - Pages: 6

Premium Essay

Should the Reference of Religion Sch as in Oath of Allegiance, Coinanage Be Eliminated?

...YourLastName 1 YourFirstName YourLastName Instructor's Name Course Title 21 March 2013 Should Public References To Religion Such As Those On Coinage And In Oath-taking Or The Pledge Of Allegiance Be Eliminated? Introduction: The court is a place where the people go against the regulations of a country they are charged and faced in the court of Law. The court is there to ensure and maintain Law and order in the republic of any country. With this in mind, it is obvious beyond reasonable doubt that we should all focus on doing the right thing else, the law catches up on one. The government of a country so to speak initiates the law. The lawmakers represent the members of parliament these lawmakers, strategies and enact laws, which are passed in parliament. These laws guide the country against its endeavors. The laws protect the minute people in the society. It prevents bias, prevents them from the harmful effects of the society. A lot of emphasis is placed on the implementation of the set or enacted Laws. The implementation process is then passed on the the police. The police represent that part of the law, the part that is always on the lookout for the wrong doors. The police go into the field; they do the manual assessment and look out for these wrong doors. Any criminal court is then taken to jail. The jail represents the rehabilitation center of these criminals. History, has seen that previously, fairness, truth, justice did not prevail. These forced many people to be......

Words: 1002 - Pages: 5

Premium Essay

Victimless Crimes

...First, I never really realized the many debates and issues America really has until this course. Some issues may seem like common sense on how to solve the problem but not everyone may be happy with every result because of their “beliefs” moral and values. I know that wearing seat beats is state regulated. The government can legally require us to wear a seat belt. Especially, if their major concern is about cutting cost and saving the lives of others. Many feel that when we allow the government to enforce these kinds of laws, we are surrendering our ability to think and act for ourselves. To be honest we have some people that seem to have no brain and this is why such laws have to be in place. It may not be fair and it may infringe on our rights a bit but it is here to balance things. Most of the time it is not very easy to determine in specific cases the right thing to do and no solutions seem obviously correct. As adults, we have experienced many situations to where we are able to decide whether we would like to follow particular rules, but for children it is undetermined in which case it is safe to let some adults decide for them. So rules like having child restraint are put into place for them so that they are protected in every measure. I know that my children will jump in the car without putting a seat belt on and I have to remind them to put it on because when they are in the back seat. I prefer them to be in a car seat with their seat belt on for my own safety reason......

Words: 339 - Pages: 2

Premium Essay

Case Law

...wish to contest official decisions on such matters as taxation, social security, and planning permission. Such specialised tribunals (which are not courts) perform the function of ascertaining and evaluating the facts relevant to a matter within their special expertise. There is almost invariably a right of appeal from a specialised tribunal to a court, but often the appeal is restricted to questions of law. 2 2. This appeal is concerned with the Tax Appeal Tribunal established by the Tax Tribunal Act 1984 (since repealed, but in force during the relevant period). By section 3 of that Act the tribunal was to comprise (as Chairman and Vice-Chairman) two barristers of at least ten years’ standing appointed by the Public Service Commission and (subsection (1)(c)) ‘such other members as may be appointed by the Minister’. Section 6(3) provided that, subject to section 8, a determination of the tribunal should be final and binding on the parties. Section 8 provided as follows: “(1) Any party who is dissatisfied with the determination of the tribunal as being erroneous in point of law may, within 28 days of the date of determination, appeal...

Words: 1626 - Pages: 7

Free Essay

Legal and Professional Implications in Nursing

...John’s refusal to accept the treatment. John was extremely upset and distressed by the nurse’s actions and verbally refused to take the drug orally. The drug was also documented to be given via the PEG tube. The incident was then witnessed by a more senior nurse who then administered the medication correctly. This incident outlines several issues concerning legal and professional accountability. According to Dimond (2011) ‘Accountability’ is defined as how far a person can be held in law to account for their actions. This seems an appropriate definition to give because a person who has to answer to the law then has a vital responsibility. Griffith & Tengnah (2008) however points out a distinct difference between ‘accountability’ and ‘responsibility’. A responsibility means a nurse can control the way they practice. Accountability on the other hand means they are answerable to a higher authority for their practice. Dimond (2011) tells us that every nurse is accountable to criminal law, civil law, the NMC and...

Words: 1077 - Pages: 5

Premium Essay

Political Science

...the value of the others Spurious relationship- a relationship between variables that reflects correlation but not causation 7. Government- intuitions that have the authority and capacity to create and enforce public policies (rules) for a specific territory and people. There are about 89,000 governments 8. Government is different from other institutions in society in that it has a broad right to force, government can make citizens do things they otherwise might not do (such as pay taxes, educate their children, carry car insurance, and pay for lost library books) 9. Social contract- an agreement among members of a society to form and recognize the authority of a centralized government that is empowered to make and enforce laws governing the members of that society Authoritarian system- a political...

Words: 1341 - Pages: 6

Premium Essay

Medical Marijuana

...Medical Marijuana Medical Marijuana Eight out of the ten states that have made medical marijuana legal saw a teen usage of marijuana decrease from 1999 to 2006. I believe that if every state were to legalize medical marijuana, the recreational use of it would go down massively. Marijuana is good for you; it can relieve multiple pain symptoms. You can never have too much, so it is not harmful like alcohol. Marijuana has never caused a death when many legal products have caused millions of deaths each year. Our government wastes millions of dollars trying to keep marijuana out of the United States each year. If medical marijuana was legal, I believe the world would just be a better place. In 2003, Canada was the first country in the world to allow doctors to prescribe patients medical marijuana. There is only a small amount of evidence that marijuana is bad for you. Medical marijuana is not harmful in anyway, it cannot kill you. There are no significant health risks. Marijuana is proved to relieve pain from arthritis; it decreases anxiety, can control epileptic seizures, slows down Alzheimer’s disease, and eases the pain of multiple sclerosis. The first marijuana based prescription was called Sativex, it came out in the United Kingdom in summer 2010. If medical marijuana wasn’t available, many people would be somewhere, useless, suffering and lying in pain. Smoking marijuana has also been known for even stopping the spread of cancer. Marijuana can stimulate an......

Words: 832 - Pages: 4

Free Essay

Koolgames Case

...Team 1: Issue/Arguing Point | Pro’s | Con’s | 3 pieces of intellectual property stolen (games) | * Put in the most effort to develop the games and company * Were the companies first three products to be launched * Could potentially increase sales in the future by getting the company’s games into the hands of consumers | * Almost-Angels has the majority (52%) stake in the company * It is KoolGames responsibility to act on the course of action * People with the unofficial games don’t know that are the creators * Publicity (for now) goes to Hot-Damn.china | Hot-Damn.china infringed on copy righted material | * Hot-Damn.china is obviously in violation of the Digital Millennium Copyright Act * Violation of the Computer Software Copyright Act * Source of infringement is traceable instead of hundreds of isolated events (peer to peer sharing) | * Has to contact the U.S. department of Commerce and file a claim/report * Might be difficult to work with the Peoples Republic of China’s Trade Ministry because of the distance. | Significant amounts of revenue lost | * Potential to make up a portion of the revenue through lawsuits and legal action | * Unlikely that all lost revenue will be reimbursed * The cost of the trial and hiring lawyers etc. * is a new company, requiring retained earnings in order to be successful * Games being sold 25% below original cost * In the time that it takes to......

Words: 332 - Pages: 2

Free Essay

Week 2 Assgn gives people a way to think about what they are about to eat by looking at the calories. When one notices that a burger is 460 as opposed to another burger at 165 calories they may rethink the 460 calorie burger. This is a great idea and I hope that this happens. Please consider this proposal because it may be a start to a healthier America. 4. This expires on 6/6/2011 5. A) Once you have submitted your comment you will be legally entitled to challenge the validity of the rule in court, if you choose to do so. B)If the proposal passes there are five legal theories that could be used to attempt to challenge the proposal. They are: 1. It is arbitrary, capricious; an abuse of discretion, or in the violation of some other law. 2. The regulation is unsupported by substantial evidence. 3. The rule that a regulation can be set aside if an agency did not comply with APA requirements of the notice, publication or public comment of the input. 4. The regulation is unconstitutional. 5. Ultra Vires goes beyond the authority given to the...

Words: 371 - Pages: 2

Premium Essay

Due Process

...No person . . . shall be deprived of life, liberty, or property without due process of law (The Courts in Our Criminal Justice System, 2003). The legal code of due process means that the government has to respect legal rights of a person who is being accused of a crime. In the United States Constitution, due process is only mentioned twice- in the Fifth Amendment and in the Fourteenth Amendment. According to the law of the land, a defendant in a criminal case is always innocent until they are proven guilty. Individuals who are accused, also known as the defendant, has to be informed of the charge or the charges that are being brought up against them. The person who is being accused of the alleged crime or crimes has the right to present their case before a jury of their peers. Due process gives the accused the right to a speedy trial. While on trial, the accused has the right to state their case and even offer witnesses if there are any available. Those who are called to testify are obligated by law. Due process is important in the criminal justice field because everyone has their own rights. Their legal rights are the most important of all. While studying history, there have been periods where there was no set laws and the world was in absolute chaos. Our rights by the law may not be perfect but nevertheless they are there to help protect us. References The Courts in Our Criminal Justice System (2003)...

Words: 254 - Pages: 2