@Carl Love That's a great solution, thank you! I indeed expect this integreal to be another distribution. I'll send you a private message to explain it more in detail. 

@John Fredsted That's exaclty what I was looking for. Thanks for your great help!

@John Fredsted Thanks again, and great that you want to have a look at my code. I uploaded it: IG_GAM_mixture.mw 

@John Fredsted Thanks for your prompt answer! Shift + Enter seems to only work in lines containing code, but not in lines containing output.