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I have many curves that I want to fit using a convolution of some functions. These functions include Weibull distributions with 2 parameters lambda and k, as well as a function B(t) such as measured curves to fit to model = F(lambda1, k1, kambda2, k2) + B(t)

The main problem here is that even if the lambda's, k's and B are not colinear, they can be "kind of" substituted and the optimization can lead to different local minima, with a close final error, but parameters not close at all.

This is a problem because I intend to interpret the value of these parameters as natural characteristics of the objects I observe.

Our actual approach is to minimize the number of parameters, i.e. fixing some of the lambda's and k's, as we would do if there were a function linking them. However this is arbitrary + this is a sacrifice as I can not interpret this parameters value anymore.

So question : is there a method / analysis / related problem / science paper dealing with this problem of unstable optimization when parameters are not exactly perpendicular degrees of liberty ?

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