In article <[EMAIL PROTECTED]>,
Dennis Roberts <[EMAIL PROTECTED]> wrote:
>At 07:34 AM 2/19/02 -0500, Herman Rubin wrote:
>>I do not see this. The binomial distribution is a natural
>>one; the normal distribution, while it has lots of mathematical
>>properties, is not.
>i don't know of any "distribution" that is natural ... what does that mean?
>inherent in the universe? all distributions are human made ... in the sense
>that WE observe events ... and, find some function that links events to
>probabilities
>all of mathematics ... and statistics too as an offshoot ... is made up
Yes, but much can be well described with mathematical
models. This has been called "the unreasonable
effectiveness of mathematics".
The idea of essentially independent events with the same
probability can, I believe, be considered natural. Thus,
the number of them in a fixed number of trials, and its
distribution, can likewise be considered natural.
On the other hand, nobody came up with the idea of something
having a normal distribution until long after the distribution
was known as an approximation to the binomial, and some other
cases of the Central Limit Theorem had been found. Gauss did
give some mathematical arguments for the distribution of
observational errors to be normal, assuming certain properties
of observational errors. These are only approximately correct.
Poincare stated that "everyone" believed in normality of
natural observations; the empirical people, because they
thought the theorists had proved it had to be the case,
and the theorists because the empiricists had found it to
be so. It is NOT so.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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