I have four time-series, of a physical quantity (heat flux). When I remove the mean value from my data points Xn = X - mean(X) and divide them with the standard deviation Xn' = Xn/std(Xn) the histograms of all cases are almost the same. What does this imply? Each simulation has increasing input of energy and the magnitude of flux increases. Thank you in advance!!
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$\begingroup$ Are your means about 0 and standard deviations about 1? $\endgroup$– DaveCommented Mar 29, 2020 at 20:32
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$\begingroup$ after removing the mean and dividing yes they are $\endgroup$– Mavridis M.Commented Mar 29, 2020 at 20:33
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$\begingroup$ What about before? $\endgroup$– DaveCommented Mar 29, 2020 at 20:36
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$\begingroup$ totally different. the first simulation has a mean almost ten times smaller in magnitude compared to the last one. Each simulation is done with increasing inputted energy. $\endgroup$– Mavridis M.Commented Mar 29, 2020 at 20:39
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$\begingroup$ When you say "the histograms are almost the same", presumably you mean the shape appears broadly the same but the axes are different. If the samples are large, this is not the least bit surprising, since subtracting a constant and dividing by a constant wouldn't be expected to change anything more than the axes (except as far as the bins would be slightly different, due to changed proximity to the round numbers typically used for the bin origin and width. $\endgroup$– Glen_bCommented Mar 30, 2020 at 14:22
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This is a standard technique for normalizing distributions of data. It seems like this implies your data comes from the same family of distributions defined by the mean and std. dev. parameters.
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$\begingroup$ that seems correct but what does it imply for the control parameter (energy) of the different simulation? $\endgroup$ Commented Mar 29, 2020 at 20:56
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$\begingroup$ Not quite sure what you mean -- it would seem that changing the control parameter doesn't affect the type of distribution, but only has some scaling effect on the parameters? $\endgroup$ Commented Mar 29, 2020 at 21:00
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$\begingroup$ yes how can I find the scaling law? $\endgroup$ Commented Mar 29, 2020 at 21:05