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I have two sets of experimental data for exponential decays of isotopes and I calculated the ratio of the two isotopes as a function of time. The theoretical model and the fit of the experimental data are respectively :

$1.04\text{e}^{-0.000856008t}$

$1.03154\text{e}^{-0.000457549t}$

The two curves are near of each other (I'm only interested in comparing the [0-110] x-range) but is there a way to calculate an error between the two curves (like a standard deviation)? I need to determine if the data are normally distributed so I thought getting the standard deviation from the theory/fit would be a correct way... Any ideas?

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If you have good reasons to believe the theoretical model, can you look at the errors in the actual data minus the corresponding data from the theoretical model? Is there a pattern in the errors, evidence of additional variables, etc? –  bill_080 Nov 20 '12 at 1:18

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You could use bootstrapping to estimate the distribution of your decay parameter. Then you test whether the theoretical parameter (+- region of practical equivalence) falls within 95% of that distribution.

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How would this bootstrap work, exactly? How do you resample from, say, a set of $(t,x)$ values? (Although there are some well-known ways, one has to make choices and assumptions. I believe that addressing my question will force you to consider assumptions about the errors in the data, which may have some relevance to the second part of the question about a normal distribution.) –  whuber Nov 19 '12 at 21:21

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