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I am running an ecosystem model and would like to give the proper statistics for a sensitivity analysis I'm performing on the model. The model provides a vector x containing all the flows in the model (i.e. x = (1200, 98.3, 12, 108.9, 0.4, 23...)) along with a vector of the standard deviation for each of those flows.

I am looking for a rigorous way to compare two of these vectors of distributions and to quantify the difference. I can make up a formula to do this easily enough, eg sum of square residuals, but doing it right and having a statical basis would be much better. Is there a test for this sort of data? I've looked a bit into MANOVAs and related but I havent seen anything that deals well with distributions rather than observations.

Hope this is somewhat clear and thanks! (I use R for all my coding btw)

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