1
$\begingroup$

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?

Improve this question
$\endgroup$
1
  • $\begingroup$ 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? $\endgroup$
    – bill_080
    Nov 20, 2012 at 1:18

1 Answer 1

Reset to default
1
$\begingroup$

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.

Improve this answer
$\endgroup$
1
  • 1
    $\begingroup$ 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.) $\endgroup$
    – whuber ♦
    Nov 19, 2012 at 21:21

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.