Peak Oil

There's this theory that oil production will go up ... then it will go down.
When things like that happen, math-types (almost) immediately assume a Normal Distribution function will fit the data:

If that were the case, then the logarithm would satisfy:
log(f) = A - K (x - m)2 ... for particular values of the parameters A, K and m

That's a parabolic curve ... so we'll try fitting such a curve to the logarithm of the Oil Production data.


We get this (where the "best" fit is the one that minimizes the Root Mean Square error between the data and the curve):
   

>What's them grey curves?
The parameters have been adjusted up or down by 1% ... to see how sensitive the "best fit" is to that kind of change.
>So ... is that a good fit?
Wait and see.
>Is that the "best" fit?
You can play with the spreadsheet below and use your own imagination as to what's "best".
I should point out that lots of people do this sort of thing:

Using Average Error as definition of "best fit"

YearProduction
196531,806
196634,571
196737,121
196840,438
196943,635
197048,064
197150,846
197253,668
197358,465
197458,618
197555,826
197660,412
197762,714
197863,332
197966,050
198062,948
198159,535
198257,298
198356,599
198457,686
198557,472
198660,463
198760,784
198863,154
198964,042
199065,460
199165,268
199265,774
199366,028
199467,104
199568,102
199669,897
199772,185
199873,538
199972,325
200074,861
200174,794
200274,431
200376,990
200480,256
200581,089
200681,497
200781,443
200881,820

>Ya know, that red curve don't look much like a Bell Curve.
We can extend it well beyond year 2060. How about this?

>Now I'm happy.