ROC curves are monotonically increasing functions $[0, 1] \rightarrow [0, 1]$ which start in (0, 0) and end in (1, 1). They are "over" the diagonal $x$.
They look a bit like $1/x$, but moved to the upper left and always above $x$.
Is there a parametrized form for such functions?
Background
I want to make a small explanation of those. This is what I have so far (code):
