This is really interesting..


Consider any list of numbers that was obtained from the financial
records of a corporate, or from geographic, scientific and
demographic data.It comes as a great surprise that, if the numbers
under investigation are not entirely random but somehow socially or
naturally related, the distribution of the first digit is not
uniform but the following: 1 will be the first digit about 30% of
cases, 2 will come up in about 18% of cases, 3 in 12%, 4 in 9%, 5
in 8%, etc.

For the more mathematically inclined - the first digit, D, appears
with the frequency proportional to log (1 + 1/D).This is known as
Benford's Law.

The astonishing fact is that this law is correct for ANY list of
meaningful numbers that are socially or naturally related. It also
astonishing that none disputes it or offers a competing law related
to digits.

The law was discovered by the American astronomer Simon Newcomb in
1881 who noticed that the first few pages of his logarithm tables
books were more worn than the last few and from this he surmised
that he was consulting the first pages-which gave the logs of
numbers with low digits-more often

In 1938, Frank Benford arrived at the same formula after a
comprehensive investigation of listings of data covering a variety
of natural phenomena.

In 1961 Roger Pinkham discovered an interesting property of the
Benford's probabilities.It turned out that these probabilities
(i.e. 30%, 18%, 12%, in 9%, 8%, etc) are scale invariant. In other
words, if a set of numbers followed Benford's law closely, and if
all the numbers in the set were multiplied by a nonzero constant
(such as 22.04 or 0.323), then the new set of numbers would also
follow Benford's law closely. Only the probabilities of Benford's
law had this amazing property.

This scale invariance explains why Benford's law works on financial
data throughout the world, even though the data are expressed in
different currencies.

Benford's law has surprising applications in financial fraud
detection. Because human choices are not random, invented numbers
are unlikely to follow Benford's law.

The interesting thing is that the more the deceivers try to make
their acts look random the easier it is for CPA's using Beford's
law to expose them.

Dr. Theodore P. Hill asks his mathematics students at the Georgia
Institute of Technology to go home and either flip a coin 200 times
and record the results, or merely pretend to flip a coin and fake
200 results. The following day he runs his eye over the homework
data, and to the students' amazement, he easily fingers nearly all
those who faked their tosses.

A person trying to fake 200 flips of a coin would never list 6 or
more series of the same side although in true randomness these
series have a quite high probability of occurrence.