I am trying to succinctly define the inverse binomial distribution. Not the normal approximation, but the real thing, which will be discrete. So far I have this:
$F^{-1}(\alpha;N,p) = k,\ \ s.t.\ \ \sum_{x=0}^k f(x;N,p)\ge \alpha$
The only thing with this is that it is the $smallest$ k which satisfies the second part above. Right now it is imprecisely defined. Any thoughts on how to write this properly?