[EMAIL PROTECTED] (dennis roberts) writes:
> in minitab, you can create a discrete distribution ... say ... numbers from
> 1 to 10 ... and then assign p values (adding to 1 of course) to each ...
> and THEN sample from that population distribution ...
The problem is, Chiu has =NOT= specified the probability distribution;
he has only specified its range, mean and variance, and the qualitative
desideratum that it ``approach normality'' in some unspecified sense.
Hence, Chiu's distribution is UNDER-DETERMINED without imposing additional
constraints.
The principle of Maxiumum Entropy which I invoked selects the unique
distribution that contains =ONLY= the Shannon information-theoretic
information-content of the constraints Chiu gave his problem statement.
If you advocate a different distribution than the MaxEnt distribution,
then you either are incorporating some additional information that Chiu
did =NOT= give in his problem-statement, or else you are using a different
definition of information than Shannon's --- which is hard to justify,
since Shannon's definition of information-content is ALMOST UNIQUELY
DETERMINED by some =VERY= general and desirable axioms...
-- Gordon D. Pusch
perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;'
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