Hello,
After fixing some bugs in FFT, I come back to this one.
I have looked at the Landau case, and this is related to a problematic definition we have in the Landau distribution.
We have an implementation of the Landau(x) as defined in the original definition,
first equation of Landau distribution - Wikipedia and implemented from code coming from the CERNLIB.
See ROOT: Probability Density Functions (PDF)
In that definition there is no location and scale parameters defined and we artificially introduce a location parameter in the code as x' = (x-m)/s.
Now this is different than the correct definition of the family of Landau distributions described as p(x;mu,c) in Landau distribution - Wikipedia.
Using that correct definition is true that:
CONV(Landau(x,m,c), Landau(x,m,c)) = Landau(x, 2*m, 2*c)
but it is not true that
CONV( Landau( (x-m)/s), Landau((x-m)/s) ) = Landau ( (x - 2*m)/s )
This explains what is observed in the plot above running the given macro TwoLandau.py gives difference results for the PDF between twomip and onetheomip.
If the same macro is applied to another stable distribution, like the Gaussian, see TwoGaus.py (4.1 KB) ,
the result is what expected, confirming that there is no problem on the RooFit side when performing an FFT convolution.
Lorenzo