# How to find the inverse of F(x), where F is a cumulative distribution function

I have a cumulative distribution function $F(x)= \mathbb P(X < x)$.

Now, for some further purposes, I need to find its inverse. The case is also that I am dealing with a KS test, where I have the implication: $\sup |F_n(X) - F(X)|$. So, what does it mean if I define the inverse of $F$ as

$$F^{-1}(y)= \min \{F(x)>y\} \>?$$

What does this represent visually? And why is it $F(x)>y$ that we are looking at? (I can see how it comes about algebraically, but I cannot visualise it).

-
The cumulative distribution function is usually defined as $F(x)=\Pr(X \le x)$, i.e. is right continuous. –  Henry Oct 23 '11 at 18:54
–  cardinal Oct 23 '11 at 22:19