# Is a gaussian distribution 'like a sine wave'

1. Jun 26, 2007

### leright

So I was having a conversation with the guy I share an office with and I brought up the gaussian distribution to show the probability distribution of energies of electrons generated by a filament. He mentioned that it 'looks like a sine wave', and I said 'sorta, but it's not a sine wave'. He said that everything in nature behaves like a sine wave and then I replied that exponentials with imaginary arguments are sine waves, but a gaussian distribution isn't really like a sine wave.

So, is there any truth to my office mate's argument, or is it irrelevant or incorrect to even bring it up?

I suppose all functions can be described by an infinite sum of sines and cosines of a spectrum of frequencies and phases angles using fourier transforms even if the function isn't periodic, but I can't conclude that this means all functions behave like sines and cosines.

Maybe I am just not understanding his argument. It was probably a waste of time to et into an argument about in the first place, but I thought I'd get your opinion.

2. Jun 26, 2007

### symbolipoint

Here is a very crude idea:
A gaussian curve should have an identifiable amplitude and identifiable period. Would a sine wave duplicate or nearly enough duplicate the points on the gaussian curve? ....
... See, I told you my idea is very very crude.

3. Jun 26, 2007

### mathman

The Gaussian curve has one max, is always >0 and tails off to 0 as x-> -oo or oo. The sine curve oscillates between -1 and +1 in a completely repetitive way. In no way do they look alike.

4. Jun 26, 2007

### leright

Yes, this is the obvious answer and is all I wanted to hear. I was just looking for a second opinion or backup opinion, since this pointless argument dragged on for a while and I wasn't really able to convince him that a Gaussian distribution wasn't really 'like' a sine wave.

Thanks for the support. :)

5. Jun 26, 2007

### ZioX

Sure it is. It's kind of wavy.

6. Jun 26, 2007

### chroot

Staff Emeritus
The two functions are nothing at all alike, as mathman says. Furthermore, a probability distribution function must have a finite integral, so a sine wave is not even a valid pdf.

In one sense, though, both sine waves and Gaussians are similarly 'special.' Sine waves are eigenfunctions of the differential equations that govern linear systems, which means that if you put a sine wave into a linear system, you get another sine wave out. Gaussians are the eigenfunctions of the Fourier transform, which means that if you take the Fourier transform of a Gaussian, you get back another Gaussian.

Since linear systems and Fourier transforms exist everywhere in nature (acoustics, optics, electronics, etc.), they are both extremely important.

- Warren

7. Jun 27, 2007

### uart

Since the above statement indicates that you are at least somewhat familiar with a Gaussian distribution I find it very puzzling that you failed to notice that it was different to a sine wave. It’s a bit like asking if a gasoline motor and a rodeo clown are sort of the same thing. It would certainly seem a strange question, but even more so if the person asking it was apparently already at least somewhat familiar with both of those items.

8. Jun 27, 2007

### leright

no uart, it was clear as day that they were different to me....but I just wanted a second opinion to demonstrate to this person I am arguing with that they are in fact different, since I can't seem to get it through his head no matter what I say.

9. Jun 27, 2007

### chroot

Staff Emeritus
Can this person draw the two functions on paper?

- Warren