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

From: Ken Knoblauch <knoblauch_at_lyon.inserm.fr>
Date: Sun, 02 Mar 2008 20:54:32 +0000 (UTC)

Johannes Hüsing <johannes <at> huesing.name> writes:

>
> 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"....
>

> 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.
>
It's not the only one. There is also the comb function, an infinite train of evenly spaced impulse functions that is its own transform, and then there is abs(x)^-0.5 and sech(x), but I'm just reading out of the appendix of Bracewell, 1978, The Fourier Transformation and Its Applications, McGraw-Hill.

best,

Ken



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