Re: [R] [OT] "normal" (as in "Guassian")

From: Johannes Hüsing <johannes_at_huesing.name>
Date: Sun, 02 Mar 2008 20:58:52 +0100

Am 02.03.2008 um 17:44 schrieb Gabor Csardi:

> I'm not a statistician, but do i remember well that among all
> distributions with a given mean and variance, the normal distribution
> has the highest entropy? This is good enough for me to call it
> "normal"....

There's more. Among all rotation-symmetric distributions, the standard bivariate normal is the only one where x and y are independent.

Also, the formula for the standard normal distribution is the only one that is its own Fourier transform. So, if we assume the same distribution for a momentum and a location of a physical object, according to Heisenberg's Law it has to be the normal.

Whereas we ought to be wary about assumption of normality for the distribution of phenomena in nature, the normal and its henchmen play a defendable role when describing summaries of phenomena, like arithmetic means. I'd even go as far as buy into Youden's hype described in that Kruskal and Stigler essay.



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