Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

[Phys-L] Fwd: Benford

Oldie but oldie! Used for detecting tax return irregularities: people dream up way to many 5's too few ones.
[From an ECN on line piece....]

Brian W

Dr. Benford discovered, in a huge assortment of number sequences --
random samples from a day's stock quotations, a tournament's tennis
scores, the numbers on the front page of The New York Times, the
populations of towns, electricity bills in the Solomon Islands, the
molecular weights of compounds the half-lives of radioactive atoms and
much more -- [something unexpected.]

Given a string of at least four numbers sampled from one or more of
these sets of data, the chance that the first digit will be 1 is not one
in nine, as many people would imagine; according to Benford's Law, it is
30.1 percent, or nearly one in three. The chance that the first number
in the string will be 2 is only 17.6 percent, and the probabilities that
successive numbers will be the first digit decline smoothly up to 9,
which has only a 4.6 percent chance.

A strange feature of these probabilities is that they are "scale
invariant" and "base invariant."