Fitting a function of the form x-a for unknown a

We have data which is roughly exponential for x<a, and approximately a power law (x-a)^b for x>a, but I'm unclear how (or if it's even possible) to find a adaptively.

Clearly fitting a function of the form Ce^(bx)+ c(x-a)^d is a problem (if for no other reason than the fact that 0<x<a gives complex value), but short of brute force trial and error to find a, I'm not quite sure where to start.

I guess I'm looking to optimize the value of a by simultaneously fitting the exponential below and the power law above until both converge (though I'm pretty sure that's not possible without a fair amount of work).

Answer 1

[Roger Wohlwend]

Yes, you're looking for an optimization, and I can assure you that it is not a fair amount of work. However it won't work with the function you mention in your question. Instead use the optimization function lsqcurvefit with the following function you want to fit:

function y = myoptfunc(coeff, xdata)
   y = NaN(length(xdata),1);
   q = xdata < coeff(1);
   y(q) = coeff(2) * exp(coeff(3) * xdata(q));
   y(~q) = coeff(4) * (xdata(~q) - coeff(1)).^coeff(5);
end

The vector coeff contains your coefficients. The first one is your parameter a.

[Shawn]

Cheers, thanks. Sorry for the delay in getting back to this, life intervened! I'll have a play with the method you suggested and see how it goes, it looks generally useful for us for some other types of fitting we need to do as well.