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Say I compute monte carlo output from input scenarios. Input are discrete time series. I choose time series as an example to make the problem more obvious - this could be also any curve.

Computation for output is performed at each time: f(input(t))=output(t). On the time line, we can distinguish severale periods with their own characteristics.

I want to compare MC outputs from two experiences. Both experiences are different in the way to compute input scenarios. For the first one, an input scenario is obtained from original time series adding to the value at each time an independant gaussian noise. For the second one, an input scenario is obtained from original time series adding to all time values in one zone the same randomly picked gaussian noise.

For both experiences, we compute output for all scenarios. Then, we average each output curve zone by zone. If there are 4 zones for instances, we have, for each of the N outputs from MC, 4 points. We compute MC distributions for these outputs.

I want to compare the distributions of outputs for both experiences, and I will use for that purpose a Kolmogorov Smirnoff test for example.

In a theoretical viewpoint though, what should I expect ? That distributions are similar ?

Please ask for precision if problem is not clear.

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