Hi Lorenzo,
Thanks for the information! I took a look at the paper you linked and I think I understand where the differences are now. The integral used by ROOT seems to be the second equation in wikipedia,
While the one in Mathematica seems to be the extension of the Landau distribution definition (the fourth equation in wikipedia) into a location-scale family. The documentation is here, although it’s quite sparse. But if you input that fourth equation and find the MPV, it matches the one used if you use the built in Landau function (thanks @gabrielrabanal for checking this!).
As said in wikipedia, the Mathematica version reduces to the ROOT one when mu = 0 and c = pi/2. So If i input 0 and pi/2 in Mathematica and scale the resulting random numbers by multiplying by the ROOT sigma and adding the ROOT mu, I get the same distribution.
