Benford's Law
F/32 Eurydice
I just looked up Benford's Law, and found that it describes the
distribution of digits in the first decimal place. http://is.gd/dnIfL
I had heard that it states that the distribution of digits is random,
in all the other places. Does this other law that I thought was
Benford's have a name?
Rob Johnson
The other digits have a slight affinity for the lower digits as does
the first digit, but the second digit is more uniform than the first,
and the third digit is more uniform than the second, etc. This is
discussed in the same article that you listed:
<http://en.wikipedia.org/wiki/Benford%27s_law#Generalization_to_digits_beyond_the_first>
if that gets broken by your browser, try
It says that the probability of d being in the n-th digit is
10^{n-1}-1
--- 1
> log ( 1 + ----- )
--- 10 10k+d
k=10^{n-2}
or, for those without monospace font capability,
sum_{k=10^{n-2}}^{10^{n-1}-1} log_10(1 + 1/(10k+d))
Rob Johnson <r...@trash.whim.org>
take out the trash before replying
to view any ASCII art, display article in a monospaced font
Robert Israel
You had heard wrong: the distribution is not quite uniform. This is
also part of Benford's Law.
See <http://en.wikipedia.org/wiki/Benford%27s_law>, section
"Generalization to digits beyond the first".
--
Robert Israel isr...@math.MyUniversitysInitials.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
spudnik
if that's not a pun.
> "Generalization to digits beyond the first".
--les ducs d'oil!
http://tarpley.net
Rob Johnson
spudnik <Spac...@hotmail.com> wrote:
>so, how about for base-3? -- not "sumorial,"
>if that's not a pun.
>
>> "Generalization to digits beyond the first".
Base 3 is pretty much the same, but using log base 3 instead of log
base 10. For base-b, he probability of d being the n-th digit
(n > 1) is
b^{n-1}-1
--- 1
> log ( 1 + ------ )
--- b bk + d
k=b^{n-2}
just as the cited article says that the probability of the first
digit being d is
1
log ( 1 + - )
b d
spudnik
can we use e? (not "sumorial?")
> >> "Generalization to digits beyond the first".
> For base-b, the probability of d being the n-th digit
> (n > 1) is:
> b^{n-1}-1
> --- 1
> > log ( 1 + ------ )
> --- b bk + d
> k=b^{n-2}
>
> that the probability of the first
> digit being d is:
> 1
> log ( 1 + - )
> b d
thus&so:
sorry; I'm going to stop saying, thence he died, and
abuzing my time with this monolog. thanks for all fish!
I'm just saying, go jumpt into a pool of spacetime, or
timespace, as long as it's deep!
> read more »...
thus&so:
yeah, but are the glasses, 3d, or the clocks -- or neither or both?
> ... so, I said, "Hey, Einstein, space and time are made of rubber!
> "Just kidding, dood."
> I am, however, not implying that he was a surfer, but
> he did know the canonical surfer's value ... of pi.
thus&so:
it's just his bot, as far as I can tell,
without researching it ... googoling would be way
too much positive feedback, and that's unpositively moderate
anyway, what difference between lightwaves and rocks
o'light, vis-a-vu the curvature of space (as
was uncovered by You now who & you know whO-oo,
in the 18th and BCE centuries (or 2nd and Minus Oneth millenia ?-)
also, don't forget the ... well, their are a few of them!
> If colleagues know, what good?
thus&so:
... time, considered to be perpendicular to all
of the three spatial directions; at least, in some abstract sense.
anyway, I invented the terminology; so ,there.... um,
perpendicular Universes:
--BP's cap™ call of brokers the group! association
http://tarpley.net