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Subject: Re: [office-comment] Re: Gaussian Distribution vs Normal Distribution

• To: office-comment@lists.oasis-open.org
• Date: Wed, 13 Feb 2008 14:53:26 +0100

```Hello all,

I am revisiting my older post with a more detailed analysis to
argue strongly against the "normal distribution"

> I strongly suggest considering some other statistical authorities as well.
>
> I remember the late prof. Feinstein strongly advocating the use of
>
> Persisting in erroneous namings is not a virtue, and IF many do it, it
> still is NO virtue, when better alternatives exist.
>
> Also, as the newer statistical methods get into common use
> (I refer here at bootstrapping procedures and other non-parametric
> tests) the so called normal-distribution will loose most of its
> appeal and usefulness. Actually, many professional statisticians
> use less and less often tests based on the gaussian distribution.
>
> ...

> > ...
> > While there are obviously other statistical distributions, I think the
> > central limit theorem is a pretty good argument for NAMING this
> > distribution the "normal" distribution.

Many authorities in the field consider the bootstrap procedures
the future of statistics. My view is the same.

Unfortunately, assigning the *normal* label to a distribution is
quite shortsighted. The truth is, NO real data will ever be gaussian,
by virtue of the finite nature of the data. At very large population sizes,
some data might approach a gaussian distribution, BUT it will be still
finite data and therefore NOT-gaussian.

Now, even IF this data is not gaussian, we can determine an *accurate*
distribution using a resampling technique.

Whatever our data is, we always can determine the distribution.

Lets say we have the following data: 1, 2, 3
[I deliberately avoid the word 'sample' - we so often have
actual groups and NOT samples from a larger population -
therefore the central limit theorem looks at least from an intelectual
point of view loony. And we don't need it at all to get our distribution.]

We can resample with replacement:
(and calculate a statistics for it if we wish, e.g. the harmonic mean)
1,1,1 - only 1 occurence
1,1,2 - 3 occurences
1,1,3 - 3 occurences
...
3,3,3 - only 1 occurence

So we got the *perfect* distribution of this data. I would call it
the *normal* distribution of this group of data because it is indeed
normal to this "sample". It *accurately* represents this data.
And it is definitely NOT gaussian.

It may loosely resemble a gaussian distribution, BUT it is definitely NOT
gaussian.

The fact is, we are able with modern computers to accurately calculate
the distribution of EVERY statsitics on any group of data
(NOT just means and the like), so there is absolutely NO need to
stick to antiquated methods and misleading procedures and terminology.

Hope this helps clarify my position as someone who has worked in the field
of statistics. And no, many statisticians I know have similar views.

Sincerely,