# Error on the integral of a fit function

Good afternoon,

Is there a function or a simple way to determine the error on the integral of a fit function in ROOT? Say, I have a function of 5 parameters each with its own error, how do I determine the error on the integral that incorporates the error on the parameters? Do I just have to do this on a case by case basis or is there a general procedure?

Thanks for the help,
-Brian

Hi Brian,

the general procedure is to apply the error propagation formula that you find in any statistics book.
You need to calculate the derivatives of the integral with respect each parameter and then multiply them by the covariance matrix that you get from the fit.

Cheers

Lorenzo

Hello all
I have the same inquiry here, I defined the crystalball fitting function, and was able to fit the curve and obtain the 5 parameters with errors.
the simplest method tho find area under the fitting curve is (Integral=(crystalball->Integral(2.,8.))/Bin_width ), where 2 and 8 are my spectrum limits.
how can I calculate the derivatives of the integral and use the covariance matrix in order to get the integral error??
I dont think that using the propagation formula is the proper choice, because the fitting function is composed from two different functions (Gauss + exp decay) for different ranges.