Curve Fitting

[Update - I read a more detailed description of Hubbert's work. One thing I missed in this article was that Hubbert added the constraint of the total size of oil reserves; in other words, the area under the production curve. That makes the point of this post a lot less relevant. See my post at http://northern-flicker.blogspot.com/2006/10/hubberts-method.html for my updated take.]

I haven’t read Hubbert’s work in-depth. I do have some experience with curve-fitting though, and can already offer a cautionary note. Generally speaking, even if you know that some data are going to end up being in the shape of a bell-curve, you can’t successfully fit the curve until the shape of the curve is already well-defined. For example, take this dataset:



Are you thinking what I’m thinking? OMG, this curve is so going to flatten. So you assume some sort of bell shape, run the data through your curve-fitting algorithm, and get something like this:



If that was a curve-fitting homework assignment, you would totally get an A. But now let’s see how the rest of the data actually turned out:




D’oh!! It's still a bell-curve, with similar shape parameters, just bigger. You can also get an excellent curve fit to these points; an outstanding one by any numerical standard.

Conclusion: even if you know the shape of a bell curve, you can’t predict the peak purely by mathematical means until it has already happened.