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

["David A. Wheeler" <dwheeler@dwheeler.com>]

(Regarding the OpenFormula specification):

Leonard Mada:
> I strongly suggest using within a standard document the more accurate and 
> complete name:
> *gaussian distribution* instead of the often misleading *normal 
> distribution*

Thanks for your comments.

"Complete to who" is a problem, though.  A quick review of available documentation suggests to me that "Normal distribution" is the standard name, and that "Gaussian distribution" is the uncommon (nonstandard) term.

Here's some pieces of evidence that convince me that "Normal distribution" is the more common term:
* Wolfram's MathWorld uses as its primary term "Normal distribution", not "Gaussian distribution", and has this to say in http://mathworld.wolfram.com/NormalDistribution.html :
'While statisticians and mathematicians uniformly use the term "normal distribution" for this distribution, physicists sometimes call it a Gaussian distribution and, because of its curved flaring shape, social scientists refer to it as the "bell curve."'
* It's worth noting that Wikipedia uses "Normal distribution" as its primary name; Wikipedia has a rule that articles should use the most common name for the article, giving more evidence that this is the right name.
* A Googlefight (showing which term is more popular on the Internet) shows "Gaussian distribution" with 943,000 references while "normal distribution" gets 14,100,100 references:
http://www.googlefight.com/index.php?lang=en_GB&word1=Gaussian+distribution&word2=Normal+distribution
We should choose the terms that are more common, generally, so that we can communicate - and by that measure "Normal distribution" wins.

In addition, since this is one of the _statistical_ functions in the formula spec, it seems appropriate to use the standard terminology used by statisticians. Wolfram's text in particular argues that the term should be "Normal 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.  This theorem states that "Under certain conditions (such as being independent and identically-distributed with finite variance), the sum of a large number of random variables is approximately normally distributed" [Wikipedia text, but this is well-known in mathematics/statistics].  Which means that when things get added up, even if they didn't start with a normal distribution, they converge towards it.

The spec _should_ include the term "Gaussian distribution" when discussing this function - that's fair enough.  But it appears to me that the standard name for this is "Normal distribution" - the alternative terminology seems to be primarily in specialty areas (e.g., physics).  We should strive for the most common term, and if there isn't an obvious common term, use the term that the primary experts use (in this case statisticians).  Either way, I think "Normal distribution" wins.

--- David A. Wheeler