Al Bartlett looked at fitting gaussians to US and world oil production in the following paper:

An Analysis of US and World Oil Production Patterns Using Hubbert-Style Curves, Albert A. Bartlett, Mathematical Geology, V32, N1, Jan. 2000.

He used three variables: the estimated ultimate recovery (EUR), the date of the peak (tM), and the width of the gaussian (S). He then minimized the root mean square deviations between the data and the fit to find the EUR. He also looked at the sensitivity of his model to changes in tM and S and the uncertainty of the EUR, as well as per capita oil production, and R/P ratios. At the end of the paper, he compares his results with those of other researchers.

So, what's your take on the linearization prediction of 2.3 trillion barrels for world URR now that you've done this analysis?

I am really impressed with equations containing constants given to 9 or 10 significant figures.  :)
Is Bartlett's paper available on the web anywhere?
That I don't know. I have a hardcopy that he gave me at the ASPO-USA conference. I can fax or mail a copy of it to you if you can't find it elsewhere.
Here's a link to it.

http://www.hubbertpeak.com/bartlett/hubbert.htm
http://dieoff.org/page187.htm

and here's an interesting discussion of linearlization and Gaussians in a presentation:

http://www-physics.mps.ohio-state.edu/~aubrecht/AAPTSU02oil.pdf

So I'm not seeing too much insight in there into why it works. I can't believe this isn't well trodden ground.