recalc Benford's law2

[Myron Tribus <mtribus@home.com>]

I thought about Benford's law again and this time used the product of 
three random numbers.  Again, in True BASIC

DIM Calc(9), Meas(9),pct(9),p(9)

FOR i = 1 to 1000
     LET x = rnd
     LET x = x * rnd
     LET x = 100000* x * rnd  ! product of 3 random numbers
     DO
        IF x < 1 then LET x = 10 * x  ! if x too small
        IF x > 1 then EXIT DO	     ! move leading digit
     LOOP
     LET x$ = str$(x)		     ! convert to string
     LET D1 = val(x$(1:1))	     ! extract leading digit
     LET Meas(D1) = Meas(D1) + 1      ! record nbr of occurrences
NEXT i

FOR i = 1 to 9
     LET pct(i) = Meas(i)/10   ! convert to %
     LET p(i) = 100 * log10(1 + 1/i) ! Benford's law
NEXT i
! Now create output
print "pct(i) = ";
FOR i = 1 to 9
     PRINT using "##.#   ": pct(i); ! observed %
NEXT i
PRINT
print "p(i) = ";
FOR i = 1 to 9
     PRINT using "##.#   ": p(i);  ! 100 * computed probability
NEXT I
PRINT

END


!======  result ==  observed pct vs computed p
pct(i) = 29.6   18.2   13.6   10.5    7.9    6.3    5.1    4.1    4.7
p(i) =   30.1   17.6   12.5    9.7    7.9    6.7    5.8    5.1    4.6

Surprising, isn't it??

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!