On Tue, 13 Jul 1999, Lucas Wiman wrote:
> >So for numbers 2^n (in Base 10), [or is it 2^p?] there are a lot more leading
> >ones than one would "expect" naievely (you would expect 1/9 to start with
> >"1", I imagine).
> Yes. Though they were talking about the exponents...
> Here are the percentages for the first 3000 powers of 2. The first collumn
> is the percentage, the second is the difference from the predicted Benford
> percentage. Weird, I would have thought that it wouldn't affect powers of
> two...
> .30110036678892964321 .00007037112494844799
> .17639213071023674558 .00030087165455550349
> .12470823607869289763 -.00023050052960705550
> .09703234411470490163 .00012233110664848727
> .07935978659553184394 .00017854054790701622
> .06702234078026008669 .00007555114964688849
> .05768589529843281093 -.00030605167925394399
> .05168389463154384794 .00053137218416255899
> .04534844948316105368 -.00040904107751407172
Benfords Law is a direct consequence of the fact that most sets of numbers
obtained by actual measurements are either resulting from exponentially
distributed data (eg. river lengths), or come from uniformly distributed
numbers, gathered from multiple ranges of exponentially distributed length
(eg. house numbers).
Since powers of numbers are just about the cleanest exponentially
distributed set of numbers you can get, it shouldn't really come as a
surprise that they fix the law:)
--
Henrik Olsen, Dawn Solutions I/S URL=http://www.iaeste.dk/~henrik/
Leonardo DiCaprio: Your social class is stuffy. Let's dance with the
ship's rats and have fun. Kate Winslet: You have captured my heart.
Let's run around the ship and giggle. (The ship SINKS.)
Leonardo DiCaprio: Never let go. Kate Winslet: I promise. (lets go)
Titanic, the Movie-A-Minute version
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