Difference of TH1::Fit between manual Const parameter and extend likelihood


My question is about TH1::Fit() function with “L” option.

I would like to fit some binned distribution with a single Gaussian distribution.
The distribution is not scaled, each bin means counts of the events in the bin.
The function is defined as TF1 func = new TF1("func", "gaus(0)");
This Gaussian function includes a parameter, Const.
This is not p.d.f. The const seems to be fitted like other parameter.
The Const is not entries but propotionaled to the entry depending on bin width.

On the other hand, with the extend log-likelihood, the total number of events is estimated with a Poisson distribution from the observed number of the events.
In the “Statistical Data Analysis” by Glen Cowan, Eq (6.46), the likelihood function is defined as:

\ln L(\nu_\mathrm{tot}, \theta) = -\nu_\mathrm{tot} + \sum_{i=1}^{N} n_i \ln \nu_i

The estimated entries seems to be sit on a special position.

What’s the difference between the two methods?
The TH1::Fit() with “L” option seems to be used the first way.
Can I use the extended binned likelihood with easy way?

Maybe @moneta or @jonas can help

you are fitting your distribution of counts with the function gaus(0), where gaus(0) is a substitute for [0]*exp(-0.5*((x-[1])/[2])**2).

You mention the option L for choosing the minimization of the utility function. What is the other method you are referring to ?


This topic was automatically closed 14 days after the last reply. New replies are no longer allowed.