This link has been bookmarked by 118 people . It was first bookmarked on 08 Apr 2006, by Dan McCrea.
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20 May 14
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noticed that pages of logarithms corresponding to numbers starting with the numeral 1
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1 is not one in nine
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All these seemingly unrelated sets of numbers followed the same first-digit probability pattern as the worn pages of logarithm tables suggested. In all cases, the number 1 turned up as the first digit about 30 percent of the time, more often than any other.
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The larger and more varied the sampling of numbers from different data sets, mathematicians have found, the more closely the distribution of numbers approaches what Benford's Law predicted.
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shawn lBenford's Law is a powerful and relatively simple tool for pointing suspicion at frauds, embezzlers, tax evaders, sloppy accountants and even computer bugs.
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F HEven more astonishing are the effects of Benford's Law on number sequences. Intuitively, most people assume that in a string of numbers sampled randomly from some body of data, the first non-zero digit could be any number from 1 through 9. All nine number
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25 Jul 08
raman srinivasan(From "The First-Digit Phenomenon" by T. P. Hill, American Scientist, July-August 1998)
Benford's law can be used to test for fraudulent or random-guess data in income tax returns and other financial reports. Here the first significant digits of true tax data taken by Mark Nigrini from the lines of 169,662 IRS model files follow Benford's law closely. Fraudulent data taken from a 1995 King’s County, New York, District Attorney's Office study of cash disbursement and payroll in business do not follow Benford's law. Likewise, data taken from the author's study of 743 freshmen's responses to a request to write down a six-digit number at random do not follow the law. Although these are very specific examples, in general, fraudulent or concocted data appear to have far fewer numbers starting with 1 and many more starting with 6 than do true data. -
03 Jul 07
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17 Jun 07
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Dow Illustrates Benford's Law
To illustrate Benford's Law, Dr. Mark J. Nigrini offered this example:"If we think of the Dow Jones stock average as 1,000, our first digit would be 1.
"To get to a Dow Jones average with a first digit of 2, the average must increase to 2,000, and getting from 1,000 to 2,000 is a 100 percent increase.
"Let's say that the Dow goes up at a rate of about 20 percent a year. That means that it would take five years to get from 1 to 2 as a first digit.
"But suppose we start with a first digit 5. It only requires a 20 percent increase to get from 5,000 to 6,000, and that is achieved in one year.
"When the Dow reaches 9,000, it takes only an 11 percent increase and just seven months to reach the 10,000 mark, which starts with the number 1. At that point you start over with the first digit a 1, once again. Once again, you must double the number -- 10,000 -- to 20,000 before reaching 2 as the first digit.
"As you can see, the number 1 predominates at every step of the progression, as it does in logarithmic sequences."
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Tom JohnsonUse this to verify data sets. Doig.
See Malcolm Browne's story in NYT Aug 4, 1998.Benford statistics validation AJ Workshop - Ver 1.0 Forensic Accounting AJWorkshop-Ver Bibliography
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Benford's Law is named for the late Dr. Frank Benford, a physicist at the General Electric Company. In 1938 he noticed that pages of logarithms corresponding to numbers starting with the numeral 1 were much dirtier and more worn than other pages. (A logarithm is an exponent. Any number can be expressed as the fractional exponent -- the logarithm -- of some base number, such as 10. Published tables permit users to look up logarithms corresponding to numbers, or numbers corresponding to logarithms.)
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Following Benford's Law, or Looking Out for No. 1
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Following Benford's Law, or Looking Out for No. 1
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Following Benford's Law, or Looking Out for No. 1
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David EubanksIn an exponentially growing number, the first digit is most likely 1.
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Paul CleaverBenford's Law is named for the late Dr. Frank Benford, a physicist at the General Electric Company. In 1938 he noticed that pages of logarithms corresponding to numbers starting with the numeral 1 were much dirtier and more worn than other pages.
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Michael MyersIn naturally-occurring numbers that represent quantities, the leading digit is more often a 1 or a 2 than any of the other possibilities, rather than equally distributed among all 9 digits.
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