I am posting this again, because there was some confusion about my earlier
post and I had not made my request sufficiently clear. I repeat the earlier
background and question, but add some clarification.
Background: Theodore Hill showed, in a paper published in Statistical
Science 1995, that if sequences of random variables $\{X\sb n\}$ are
selected at random in a scale (base) unbiased way, then the mantissa
distributions of the combined sample will converge to Benford's law---a
random probability measure being said to be scale (base) unbiased if its
expected distribution is scale (base) invariant.
I wondered if anyone knows of a sensible way of producing such sequences,
assuming that one has available a "good" source of uniform deviates?
Clarification:
(1) I am not, as was hinted (!), interested in defrauding the IRS. For those
who are curious, details of the fraud detection methods are described in a
number of specialist journals and also in Hill's article for American
Scientist. Cheating them requires only that one be able to create a sequence
that conforms to Benfords Law.
(2) Creating a sequence of numbers that conforms to Benfords Law is
trivially easy and no big secret. See
http://www.doc.ic.ac.uk/~jjh97/suprema/main_page.html It takes about 4 lines
of Mathematica code.
However, I am not interested in just producing a BL sequence. I would like a
constructive method of "choosing sequences of random variables, selected at
random in a scale (base) unbiased way". ... assuming a good source of
uniform deviates.
Cheers,
Mark
------------------------------------------------------------------------
Mark R Diamond
Vision Research Laboratory
The University of Western Australia
Nedlands WA 6907
AUSTRALIA
nospam email: markd at psy dot uwa dot edu dot au
------------------------------------------------------------------------
Disclaimer: The views expressed herein are solely attributable to the
author and do not necessarily reflect the views of the Department of
Psychology or The University of Western Australia.
------------------------------------------------------------------------
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