Re: trendline gaussian
Quote from Dave.Kimble@Liz
Why did Hubbert use a probability function to fit a times series? It was a case of trying the easiest thing first.
Not previously knowing anything about this science I have just done a web search. I know I am being pedantic, but Hubbert did not use a probability distribution to fit a time series. He most likely used simple arithmetic to calculate the data and then plotted the points on a graph and draw a curve through them that had a 'characteristic' shape. No formulae have been given (that I can find). To fit the curve subsequent analyses have used a Gauss or Normal curve, but it is not a distribution, it is simply a mathematical equation that 'fits' the data.
The key words are 'probability distribution' vs 'curve fit' they are not the same.
In fact the drawings of his original curve suggest that a very wide stdev is required to get the wide curve at the top of the curve, but there are the problems that the tails are ill defined. Can it be considered that oil production had a specific start date? I suspect that it is a long way before the data that is being analysed.
I could keep going, because it intrigues me, but it will not help you solve your problem and it is not a primary issue for this forum (and I am sure there are many others more qualified in this subject to comment)!
However, on the use of R2 have a look at this article it gives an example of why simply searching for a function taht fits is not necessarily the best approach.
With respect to your problem I presume that you are doing an analysis for several data sets and will hen combine the curves to provide a revised estimate of the global or regional peak oil prediction. An interesting problem and one that does appeal to my analytical mind!
With respect to your question on developing the solver, have a look at the attached workbook. You should only edit coloured cells. Note that the formulae used for the curves are all filled down the coloured columns that correspond to the graph and the titles of the curves.
I have put starting values in that help the solver. It is clear that the solver has limitations, I had to do a lot of the adjustments manually, especially for the Gamma distribution.
Note that you can not modify a cell other than the cell holding a function, therefore the solver will always need to be run as a macro.