How to get error on point and integral calculated with TF1

Roofit and RooStats
1

Hi! I would need to calculate the integral and individual points through a TF1. I would need to provide the error regarding the Integral and the individual points. I saw that there is a work aroung using the confidence levels at least for the individual points. However, I would prefer something more “straight” forware. Any suggestion how to do this? If not, maybe it would be useful to implement such error calculation in ROOT?

Bets regards

2

Hi,

Can you please elaborate more on what you would like to do exactly ? It is not very clear to me…

Suppose you have a function y = f (x | p) where p is a vector of parameters and you have a covariance matrix describing the p uncertainties.
Do you want to compute the uncertainty on the integral of f and the error on the y values ?

Lorenzo

3

Hi! No I have no covariance matrix. I am taken the parameters from a power law fit from a paper. [0] *powe(x/1000,[1]). In order to plot the linee I use TF1 defining defining [0] and [1] and their errors. Lets say that the fit is valued within the range from 200 to 10000 but I would like to calculate the integral above 300 GeV, I can call TF1::Integral(300,10000) and this would give me the integral. However, I would need to know the statistical error on this value, knowing the errors of [0] and [1]. Similar to this, I would need to know the value at 300 GeV. I do this calling TF1:Evaluta(300). But again, I would also need to know the error of this value. Of course you can to this manually calclating the derivatives with respect to [0] and [1] and then calculating performing simple error propagation, but I was hoping to find a way to get these balues directly from ROOT since I define the formula, the parameters and their errors.

4

Hi!

Any news on my “problem”?
Best regards

C

5

You should retrieve the covariance matrix from your fit and then pass it to the TF1::IntegralError procedure.
If you cannot get the covariance matrix at all, try: Error on Integral of function not Resulting From Fit

BTW. Your function’s formula seems to be quite simple so, if you do not have any information about the covariance matrix, I think you can calculate both the integral and any errors analytically.