I'm currently stuck in a small part of a proof. Namely, if we have a non-degenerate non-degenerate distribution function distribution-theory, $F$, where
$F(ax+b)=F(cx+d)$
is valid, then $a=c$ and $b=d$.
I was trying some things with the generalised inverse generalized-inverse, but since we have not assumed that $F$ should be strictly increasing, then it did not lead me anywhere. I don't expect it to be very complicated, but now I'm all out of ideas.
Thank you all!