parameter estimation of predefined function

Hi everyone, I have a function defined as following:

I'd would like to know if there is a Matlab function that can estimate these two parameters given a set of values of (x,y).

With kind regards,

Winn

[Matt J]

given a set of values of (x,y).

Are you not also given E(x,y)? You would need that, too.

[Win co]

good remark! Indeed, E is given too.

Answer 1

[Matt J]

There is lsqcurvefit in the Optimization Toolbox and nlinfit in the Statistics Toolbox. If you have neither, there is fminspleas ( Download ). The latter could be useful, because your model is loglinear in beta

   log(E)-log(1-y) = beta*f(x,alpha)

which fminspleas can advantage of. In particular, fitting log(E)-log(1-y) with fminspleas only requires a good initial guess for alpha. The solution fminspleas gives you for both alpha and beta can then be used as initial guesses in a more refined fit.

[Win co]

Thank you so much for this indication. It resolves my problem as I wished.