I have a set of data points {x(adsbygoogle = window.adsbygoogle || []).push({}); _{i},y_{i}} where each y_{i}is a Gamma distributed variable where both the shapekand scale [itex]\theta[/itex] depend on i.

I then fit the data points with a power law model y=a(x)^{b}.

I would like to know the probability distributions for the fit parameters a and b.

Is there an analytical approach for this problem? The only method I can think of is to simulate a bunch of data sets and manually build the distributions of a and b, at which point I could fit the distributions.

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# Model parameter distributions from Gamma distributed data

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