Benford’s Law Essay

Benfords faithfulness, aka first-digit law, states that in lists of numbers of naturally occurring data, the leading digit is distributed in a specific, non-uniform way. In number sequences, most people assume that in a string of numbers sampled randomly all nine numbers would be equally potential for the leading digit. Benfords fair play states otherwise. He found that the number 1 will appear first about 30% of the time and the number 9 will only appear first around 4.5%. Naturally occurring can be anything from check amounts or stock prices to lengths of rivers.Benfords law is both plate invariant and base invariant. If something is scale invariant that means if you multiplied every number in the list by the same constant, it does not significantly agitate the distribution. For example, it does not matter whether the numbers are based on the dollar prices of stocks or their prices in Yen or Euros. Mathematicians have found that the larger and more varied the sampling of numbe rs from different data sets, the more closely the distribution of numbers approaches Benfords righteousness.Benfords Law does have limitations. Benfords Law does not apply to uniform or non-naturally occurring data sets. Examples of non-naturally occurring data sets are made up of pre-assigned numbers like zip codes or UPC numbers. Benfords law can only be applied to data that are distributed across multiple orders of magnitude. Moreover, if there is any cut-off which excludes a portion of the underlying data preceding(prenominal) a maximum value or below a minimum value, then the law will not apply.Benfords law has many applications. some(prenominal) countries, states, large corporations and accounting firms use come upion software based on Benfords Law. Benfords Law is used in the accounting profession to detect fraud. It can be a powerful and simple tool for detecting frauds, embezzlers, tax evaders, inaccurate accounting and computer glitches. Dr. Mark Nigrini used Benfords Law to test the first digit in approximately 170,000 IRS model files. Dr. Nigrini found that these lines follow Benfords Law very closely. He then used Benfords Law on fraudulent data taken from Kings County, New York District Attorneys Office. The fraudulent data consisted of cash disbursements and payrolls, none of which followed Benfords Law. In general, Dr. Nigrini found that fraudulent or concocted data have far less numbers beginning with 1 and far more numbers beginning with 6 than true data do.