Sunday, February 24, 2008

Two Laws That More People Should Know About

I knew about them when I was in my early 20's and I wished I had known about them earlier.

The first is Zipf's law, which "...states that given some corpus of natural language utterances, the frequency of any word is inversely proportional to its rank in the frequency table. Thus the most frequent word will occur approximately twice as often as the second most frequent word, which occurs twice as often as the fourth most frequent word, etc."

It's a special case of the general power law distribution which many natural phenomena seem to exhibit.

The other law is Benford's law, which "...states that in lists of numbers from many real-life sources of data, the leading digit is 1 almost one third of the time, and larger numbers occur as the leading digit with less and less frequency as they grow in magnitude, to the point that 9 is the first digit less than one time in twenty. This is based on the observation that real-world measurements are generally distributed logarithmically, thus the logarithm of a set of real-world measurements is generally distributed uniformly."

Benford's law is applicable to "... a wide variety of figures, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature). "

Benford's law is also used successfully to detect accounting frauds, scientific frauds, electoral frauds, and other types of frauds. Just google for "fraud detection benford" and you will see a lot of examples.

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