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February 12th, 2009, 02:11 AM   #1
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fit one nonlinear function to four datasets

Dear all,

I encountered a math problem when trying to find a set of robust and accurate parameters for a PDF, a nonlinear function with 3 parameters. The problem is:

I have 4 datasets (X1,Y1), (X2,Y2),(X3,Y3),(X4,Y4) for a certain distribution. Each set, (Xi, Yi), contains about 400 data and was obtained from a different observational experiment. So it is assumed that different datasets should have different error variance. I am trying to use nonliner regression to obtain an empirical function from the four data sets. As the variance in each data set is unknown, it is impossible to obtain a weighting coefficient if i put them together. Is there any other solution for this case ?

The empirical function is a*X^b/(1+exp(c*X)).

I will appreciate very much if some could give me some support. Thank you!


Sam
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