[SOLVED] best fit of exponential function

Hi,
I am looking to fit a set of data with the following exponential.

y = a + b*exp(-x/c) + (d*x/c)*exp(-x/c) with x>0.

So i would like to find the best four values for the parameters a to d.
I am trying to work out something with a least squares method but I am not sure how to start (problems with how to weight y). Does anyone have an idea here?

Any answer would be highly appreciated!

Quote:

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Originally Posted by roeppieroeppie

Hi,
I am looking to fit a set of data with the following exponential.

y = a + b*exp(-x/c) + (d*x/c)*exp(-x/c) with x>0.

So i would like to find the best four values for the parameters a to d.
I am trying to work out something with a least squares method but I am not sure how to start (problems with how to weight y). Does anyone have an idea here?

Any answer would be highly appreciated!

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This calls for a numerical approach. Using a simple derivative-free method (Nelder-Mead) might be enough. In Matlab this is implemented as "fmins". Redo the computation a number of times to see if the solution depends on the start data (there may be more than one solution for such a problem).

A fancier method would be a Gauss-Newton method - it requires more programming, however.