# Uncertainty from equation involving fitted parameters [closed]

I want to estimate the uncertainty of a calculation which involves a quantity from a fitted mathematical model. More specifically, the end calculation would be something like:

P = x / A_tot

where I know the uncertainty of the x quantity. Given the uncertainty of A_tot I could then estimate the uncertainty of P with standard error propagation techniques. The problem is that A_tot is given not by experiments but comes from a fitted model with the following form:

where f(r) is a Gaussian distribution:

rp and sp are the fitted parameters, for which I have the confidence intervals, and r the independent variable.

From my model I only get a value of A_tot, which is that obtained with the best guess of my parameters. How can I estimate the uncertainty of the value of Atot so that I could use it in my final error estimation? Or should I consider it as a constant?

• Because the numerator is always infinite--the integral diverges towards $+\infty$ at the lower limit--it's difficult to proceed except to reply something like "the uncertainty is always infinite" or "this makes no sense at all." – whuber Feb 25 '19 at 13:40
• Thanks for the feedback. I have editted the question and hope it's more clear now. – egil137 Feb 25 '19 at 15:25
• There must still be something wrong with your statement of the model, because the numerator is always divergent, no matter what the fitted parameters may be. – whuber Feb 25 '19 at 15:52
• well the model is widely used in the literature. I take it that this model doesn't allow for an uncertainty calculation of its results then.Thank you. – egil137 Feb 26 '19 at 14:00
• I urge you to make a detailed comparison of the formula you have presented and what you find in the literature. I doubt there is any literature on a model that cannot exist mathematically! – whuber Feb 26 '19 at 14:07