# Fitting histograms and error propagation

I am new to fitting histograms and as a result i have an issue understanding what to consider as error propagation when calculating a quantity. The following diagram shows entries for 4 different x-ray sources resulting in for different data files generating 4 histograms which are fitted separately. Lets say i want to calculate the quantity u= a*channel for the Rb source (check the following diagram). If i wanted to calculate an error propagation as well based on the results of the fit model what should i consider as error for the Rb channel value. Should i use the $$\pm$$ values? or the sigma value or both? The well known error propagation formula is the following:

$$σ^2_u = \left( \frac{\partial u}{\partial (channel)} \right)^2 σ^2_{channel}$$

Is this formula too simplistic for this? Can i apply it here?

P.S. First 3 values on every pad refer to the histogram. We are interested in lines 4-7 which refer to the fit.

P.S.2 The diagram is generated using CERN root framework.

• Welcome Chris. You should gave more detail so readers don't have to reverse engineer what "Mean", "Std Dev", "Constant", "Mean" (again), and "Sigma" are. It would also be good to identify the physics goal of what you are doing, the specific isotopes, the detector, and the software. Dec 10, 2022 at 2:06
• This is a bit confusing. You have 4 graphs on the same plot that are all being fit separately? You already have best fit parameters with error bars and chi2/dof. The uncertainty on a parameter should be the range that causes chi2 to increase by 1. The formula for $\sigma_u$ is correct, except: what are $u$, $x$ and $y$?
– JEB
Dec 10, 2022 at 2:24

## 1 Answer

Your data seem to be reasonably gaussian, so I would say that it is ok to consider the standard deviation of the distribution as an estimate of the error in the number of channels.

Alternatively, you can plug the samples that you used to generate the histograms directly into the formula for the quantity $$u(channel)$$ and see how that distribution looks. You can get the error on $$u$$ from the standard deviation of the distribution of $$u(channels)$$.