I have an equation which reads
y=log[f(x)+g(x)]
whereas f(x)=(k1x)^n1/[1+(k1x)^n1]; g(x)=(k2x)^n2/[1+(k2x)^n2].
I want to make parametric sensitivity analysis about "log(f+g)". But it appears hard to do using an analytic method.
Can anyone help me with it? Thank you.
I assume that indeed you have a nonlinear least squares problem and your problem is to determine the sensitivity of the four parameters k1,n1,k2,n2 against noise in y. this is determined by the Jacobian of your model and the residual size. hence you must first solve the least squares problem (numerically) there are codes for this which also deliver you the Jacobian and its condition number. But the error bounds are often too pessimistic. hence my advice: solve the problem numerically, then disturb in several different manners your y values in the order of the assumed noise and resolve. this done systematically gives you a good impression what to expect. for codes look here : http://plato.asu.edu/guide.html in the section problems/least squares
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