If I have a distribution F on the random variable Y, and if I set :
$$ F^{-1}(y) = \inf \{ t \in \mathbb R : F(t) \geq y \} $$
I think it also gives a distribution on another random variable.
Is it true ? Can someone give me an example of what the graph of such distribution would look like ? When the fonction the continuous and strictly increasing, it is easy because of the bijectivity. But what happens if the function is constant on a given interval or if it isn't continuous ? I'm stuck on such things.
My reputation is to low to give a comment (so sorry to give an answer, but it's my only way to communicate with you). I answered to a question that may be helpful for you (even if it's not completely your question). See here.