Herman Rubin wrote:
>
> In article <[EMAIL PROTECTED]>,
> burt <[EMAIL PROTECTED]> wrote:
> >A casino that I frequent has a "bad beat" jackpot in its poker room.
> >Without going into all the rules, suffice it to say that the chances of
> >anyone's hitting the jackpot within any two minute interval is probably
> >of the order 10**-6. In other words, hitting the jackpot can definitely
> >be construed as a rare event. The jackpot had not been hit in about four
> >months, until last weekend, when it was hit two times in 12 hours. This
> >phenomena has happened before--several months without being hit, then
> >bam, it is hit twice in a few hours. Isn't this a characteristic of a
> >Poisson process? A very rare event goes a long time without occurring,
> >then it occurs several times within a short period.
> >Could one test the hypothesis of this "bad beat" jackpot following a
> >Poisson distribution using a goodness-of-fit test??
>
> This is not the characteristic of a Poisson process.
Herman is of course correct in one sense; but the description given
_is_ characteristic of the human perception of a Poisson process. The
human brain tends to err on the side of clustering, and perceives a
Poisson process, whether spatial or temporal, as clustered, while
labelling as "random" processes that are in fact somewhat uniform.
Readers will recall -maybe have done- the experiment in which some
students are asked to make up random strings of 1's and 0's while a
control group toss coins. The runs test then separates the sheep from
the goats; made-up strings have a bias away from long runs.
If one takes "long" and "short" as subjective labels meaning "longer
than The Standard Untrained Human would have expected" and "shorter
than TSUH would have expected" then yes, Poisson processes are
characterized by "long" periods of nothing happening followed by
multiple occurrences within a "short" time.
-Robert Dawson
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
