Introduction:
The very famous Benford’s law of anomaly detection or fraud detection does not only have application in USA’s tax department to find tax evading citizen or corporates rather it is applied on every type of mathematical series or pattern wherein objective is to find outliers in the curve of normalcy.

Few examples of its applications:
Finding right rhythm in songs to finding fake social media accounts or bots and the very recent use to find accuracy in reporting of COVID-19 cases and deaths to device strategies for virus control, it was used to screen countries’ daily records for possible misreporting by applying Benford’s law which could l pick up unreliable numbers resulting from error, oversight or manipulation. ( Source: Benford analysis of Covid-19 data By Andrew Jackson of Switzerland and Malcolm Sambridge of Australia; http://jupiter.ethz.ch/~ajackson/benford.pdf). Benford’s law has potential to apply every facet of mathematical life !

So , What is Benford law ?

Benford’s law states that in listings, tables of statistics, etc., the digit 1 tends to occur with probability ~30% , much greater than the expected 11.1% (i.e., one digit out of 9). Benford’s law can be observed, for instance, by examining tables of logarithms and noting that the first pages are much more worn and smudged than later pages (Newcomb 1881). While Benford’s law unquestionably applies to many situations in the real world, a satisfactory explanation has been given only recently through the work of Hill (1998).

How did Benford law came into existence or discovered ?
It is credited to common sense or sharp observation of Canadian-American astronomer Simon Newcomb back in 1881,noticed that in logarithm tables or log book so we used to call it the earlier pages (that started with 1) were much more worn out by the users in comparison to later other pages and published his observations to propose a law that the probability of a single number N being the first digit of a number was equal to log(N + 1) − log(N). And then in 1938 a physicist named Frank Benford tested Newcomb’s proposed law on data from 20 different domains and was credited for it. This discovery was later named after Benford.

Benford’s application also time and now inpires writers of Netflix amd others to use it in the web series and movies plot to help solve the mysteries of the case in case in question. And no doubt is the inspiration for me as well to read about the law and create this post.

• Benford’s law is used to analyze a cartel member’s financial statements and find that it is being defrauded in the Netflix series Ozark.
• Benford’s law was used to help solve a series of high burglaries in “The Running Man” episode (2006) of the television crime drama NUMB3RS.
• Benford’s law is used to expose the theft of funds from a robotics company in the 2016 movie The Accountant.

Proof of its applicabality and effectiveness can be understood from the fact researchers have a dedicated conference in the name of Conference of Benford law and in these conference data scientists meet and share the data and real world examples to showcase and co learn pros and cons of applying the law.

No more Catch me if you can, if there is a mathematical series and history of data set Benford’s law will catch you !