In article <[EMAIL PROTECTED]>,
Dennis Roberts <[EMAIL PROTECTED]> wrote:
>not to disagree with alan but, my goal was to parallel what glass and
>stanley did and that is all ...seems like there are all kinds of
>distributions one might discuss AND, there may be more than one order that
>is acceptable
>most books of recent vintage (and g and s was 1970) don't even discuss what
>g and s did
>but, just for clarity sake ... are you saying that the nd is a logical
>SECOND step TO the binomial or, that if you look at the binomial, one could
>(in many circumstances of n and p) say that the binomial is essentially a
>nd (very good approximation).. ?
>the order i had for the nd, chis square, F and t seemed to make sense but,
>i don't necessarily buy that one NEED to START with the binominal
>certainly, however, if one talks about the binomial, then the link to the
>nd is a must
I do not see this. The binomial distribution is a natural
one; the normal distribution, while it has lots of mathematical
properties, is not.
As Alan McLean wrote, the normal occurs naturally as an
approximation to the binomial, and it was only decades
later that it became an important distribution. Gauss
attempted to justify it as a distribution of errors on
theoretical grounds, but there are flaws with the
underlying assumptions, not with the mathematics.
The normal distribution is an approximation to much more,
and also methods based on the normal distribution are
often robust, in the sense that they do well for other
distributions. But converting observations or scales
so the results will be normal, or even approximately so,
should be considered a major error anywhere. Quetelet's
naming of it as "the distribution of a normal man" is
just plain wrong.
>At 06:36 PM 2/17/02 -0500, Timothy W. Victor wrote:
>>I also think Alan's idea is sound. I start my students off with some
>>binomial expansion theory.
>>Alan McLean wrote:
>> > This is a good idea, Dennis. I would like to see the sequence start with
>> > the binomial - in a very real way, the normal occurs naturally as an
>> > 'approximation' to the binomial.
--
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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