Re: Benford's Law

[Myron Tribus <mtribus@home.com>]

At 4:54 PM -0500 11/30/00, Kromkowski@aol.com wrote:
>Any thoughts about the use of Benford's law to ferret out faked data. (<A
>HREF="http://www.newscientist.com/ns/19990710/thepowerof.html">The Power of
>One</A> is a quick and dirty summary of its use.)

Prompted by John's post, I wrote the following program in True BAsic 
to generate a set of numbers

========= begin program ==========
dim X(1000), y(1000), z$(1000), N(0:9), LDigit(1000), p(0:9)
for i = 1 to 1000  ! Generate 1000 pairs of numbers
let x(i) = rnd     ! from table of random nbrs
let y(i) = rnd
let z$(i) = str$(int(100000 * X(i) * Y(i))) ! Take their product
let LDigit(i) = int(val(z$(i)(1:1)))  ! and look at the leading digit
let N(LDigit(i)) = N(LDigit(i)) + 1  ! count number of times
next i								 ! 
this LDigit occurs
for i = 0 to 9
let p(i) = N(i)/1000              ! compute the fraction
print p(i);",";                       ! display result
next i
end
============== end program =======
RESULT:
! 0 , .271 , .195 , .134 , .108 , .093 , .077 , .053 , .04 , .029
Prediction of Benford's law
       .30,    176    -----left for student exercise ---      .046
Not bad, eh?

Try multiplying two large numbers together and you will see why the 
leading digit is more likely to be a "1" than a "9".

Myron Tribus,  350 Britto Terrace,  Fremont, CA 94539
Ph:510 651 3641  Fax: 510 656 9875   e-mail: mtribus@home.com
(Quality Consultant's Prayer) Dear Lord, grant me patience.  RIGHT NOW!