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parameter estimation using fn involving root

parameter estimation using fn involving root

parameter estimation using fn involving root

I have two equations for the same dependent variable, Y1 and Y2 say. Y1 depends on x say and needs a S value that satisfies both equations,

Y1(x,S) and Y2(S) but Y1 = Y2 at a particular value of S.
Y1(x,S)-Y2(S) = 0 when S is the correct value.

I use the root(Y1-Y2,S) method to find an appropriate value of S. That part is ok. I then feed that S value back into the equation for Y2(S) to evaluate Y2.

I now have observations (y data) to which I can fit the equations to. Y1(x,S) has one parameter u0 and Y2(s) has one parameter u1, say. I wish to estimate these two parameters to obtain the best fit to the data.

The function I would like to fit looks like,

Y2(root(Y1-Y2,S))  where Y1 and Y2 are expressed in terms of their x, S and u.

I don't think the genfit() method works on this function with a root. Perhaps there is another way?

Any tips will be greatly appreciated.



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