Supposing that I have a given function that explains some behavior of one determined system. That function, has four parameters on it, which are constants that might change depending on the environment of the scenario in which the model is applied.

So, I have a set of real data and I want to find out which value of each of these parameters are able to better fit on my data. Hence, my goal is to by using my real data, discover which are the constant parameters that when applied to my function - which in theory explains the system - are able to achieve closer results to the real scenario.

So to sum up, I want with my real data, find out which are the values of the constants in my function for that particular case.

Hope that I managed to be precise and succinct albeit the complexity of the problem.

  • $\begingroup$ What is your preferred statistical software or programming language? $\endgroup$ – James Phillips Jan 6 at 12:38
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    $\begingroup$ @JamesPhillips Python $\endgroup$ – Marc Schwambach Jan 6 at 13:06
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    $\begingroup$ One of several Python options is to use scipy's differential_evolution genetic algorithm module. I use this module to generate initial parameter estimates when curve fitting, and can supply an example if it might be useful. In effect, you supply ranges for the values and the genetic algorithm makes a thorough and gradient-free parameter search within those bounds. The search bounds can be generous. It is much easier to supply ranges for the parameters than to supply specific values for them. $\endgroup$ – James Phillips Jan 6 at 15:25
  • $\begingroup$ @Marc Schwambach. Your question is much too wide. This is a so-called "Regression" kind of problem, often "Non-linear regression". You can find on the web a lot of papers dealing on this subject. One cannot give you a specific answer without knowing the kind of function in which four parameters are involved. $\endgroup$ – JJacquelin Jan 9 at 8:11

it depends on the signification of the parameter if for example 'a' is a parameter depends on the mean so you should find a rough estimation for the mean.

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