Normalization of RooExtendPdf defined in different x ranges

Dear RooFit experts,

I’ve come across a problem concerning the normalization of RooExtendPdfs when defining different x-Axis ranges:

First, if I build an extended RooGaussian pdf in a certain x range with fixed coefficients and normalization I can evaluate the fraction, “frac”, of the integral in a sub-range of x with respect to the
total integral of the pdf (which is obviously 1). If I build a new extended RooGaussian pdf in this sub-range and use the same coefficients as for the first pdf I get exactly the same curve if I scale
the normalization with “frac”. So far so good, this is exactly what I would expect. The script “test.C” reproduces this issue: test.C (1.92 KB)

But now if I try the same with a more complex pdf I do get different results. The script “test2.C” reproduces this issue: test2.C (3.21 KB)

In the second pdf I apply a convolution and a substituion of x with a RooFormula, so I suspect I do something wrong here which might cause the problem. I’d be very grateful if you could have a look at

Many thanks in advance for any comment,

Hi again,

Wouter kindly provided a solution for this issue.

The problem is that the fraction coefficient in a RooAddPdf is interpreted to be the fraction in the defined range of the observable x. So if the model is defined in a modified observable range the fraction coefficient would have to be redefined. Otherwise the mixture of the pdfs in the RooAddPdf and consequently the shape of the model is different.

However, there is a command that fixes the interpretation of the fraction coefficient to a user-defined observable range regardless of the actullay defined observable range:

where refrange is the range that is used for interpretation of the fraction coefficient.

Many thanks to Wouter for helping!