Question about error from TFractionFitter

[hugo_leung]

Hi
I am playing with TFractionFitter and trying to understand the uncertainty in the fit parameter. I generated a “data” histogram with 3 Gaussian components, then fit this histogram to the three Gaussian. I then repeated the fit 10000 times and plot the difference between the input fraction and fit result normalized by the uncertainty.

What I found is that for the first two components, the normalized difference distribution can be described with a gaussian distribution with a sigma of 1.

But the third component has a sigma way less than 1.

Is there something I did wrong, or is TFractionFitter overestimating the error on the third component.
toyMC.c (3.3 KB)

[moneta]

Hi

This is a known problem of TFractionFitter, there is a note written some time ago, see
[0803.2711] A pitfall in the use of extended likelihood for fitting fractions of pure samples in mixed samples. Figure 1 in the note illustrates well the problem.

See as well the discussion in

TFractionFitter Errors

Hello, I am currently trying to use the TFractionFitter to extract signal and background components from a pseudo data histogram. But somehow, the pull distributions have a sigma, which is less than one, thus showing that the errors are bigger than expected. I tried to make the fit easier by using two Gaus functions, but still the same problem remains. So in my script I produce two Gaus functions to create signal and background histograms, where I also draw pseudo data from the histograms for…

Lorenzo